Games
http://www.mdpi.com/journal/games
Latest open access articles published in Games at http://www.mdpi.com/journal/games<![CDATA[Games, Vol. 8, Pages 7: Social Pressure and Environmental Effects on Networks: A Path to Cooperation]]>
http://www.mdpi.com/2073-4336/8/1/7
In this paper, we study how the pro-social impact due to the vigilance by other individuals is conditioned by both environmental and evolutionary effects. To this aim, we consider a known model where agents play a Prisoner’s Dilemma Game (PDG) among themselves and the pay-off matrix of an individual changes according to the number of neighbors that are “vigilant”, i.e., how many neighbors watch out for her behavior. In particular, the temptation to defect decreases linearly with the number of vigilant neighbors. This model proved to support cooperation in specific conditions, and here we check its robustness with different topologies, microscopical update rules and initial conditions. By means of many numerical simulations and few theoretical considerations, we find in which situations the vigilance by the others is more effective in favoring cooperative behaviors and when its influence is weaker.Games2017-01-1481Article10.3390/g801000772073-43362017-01-14doi: 10.3390/g8010007María PeredaDaniele Vilone<![CDATA[Games, Vol. 8, Pages 6: Acknowledgement to Reviewers of Games in 2016]]>
http://www.mdpi.com/2073-4336/8/1/6
n/aGames2017-01-1181Editorial10.3390/g801000662073-43362017-01-11doi: 10.3390/g8010006 Games Editorial Office<![CDATA[Games, Vol. 8, Pages 4: A Nobel Prize for Property Rights Theory]]>
http://www.mdpi.com/2073-4336/8/1/4
This article provides a brief overview of the Property-Rights Theory of the firm, pioneered by Grossman and Hart (1986) and Hart and Moore (1990), and situates the theory in other literatures.Games2017-01-0481Editorial10.3390/g801000442073-43362017-01-04doi: 10.3390/g8010004Richard Holden<![CDATA[Games, Vol. 8, Pages 3: Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies]]>
http://www.mdpi.com/2073-4336/8/1/3
Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of belief-revision policies are beliefs, not strategies and acts. Thus, the rationality of belief-revision policies is subject to Bayesian epistemology. The components of any belief-revision policy are credences constrained by the probability axioms, by conditionalization, and by the principles of indifference and of regularity. The principle of indifference states that an agent updates his credences proportionally to the evidence, and no more. The principle of regularity states that an agent assigns contingent propositions a positive (but uncertain) credence. The result is rational constraints on real people’s credences that account for their uncertainty. Nonetheless, there is the open problem of non-evidential components that affect people’s credence distributions, despite the rational constraint on those credences. One non-evidential component is people’s temperaments, which affect people’s evaluation of evidence. The result is there might not be a proper recommendation of a strategy profile for a game (in terms of a solution concept), despite agents’ beliefs and corresponding acts being rational.Games2017-01-0381Article10.3390/g801000332073-43362017-01-03doi: 10.3390/g8010003Ashton Sperry-Taylor<![CDATA[Games, Vol. 8, Pages 1: Cognitive Hierarchy Theory and Two-Person Games]]>
http://www.mdpi.com/2073-4336/8/1/1
The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory.Games2017-01-0381Article10.3390/g801000112073-43362017-01-03doi: 10.3390/g8010001Carlos Gracia-LázaroLuis FloríaYamir Moreno<![CDATA[Games, Vol. 8, Pages 2: Economic Harmony: An Epistemic Theory of Economic Interactions]]>
http://www.mdpi.com/2073-4336/8/1/2
We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We show that the aforementioned minor epistemic modification of the concept of utility is quite powerful in generating plausible and successful predictions of experimental results, obtained in the standard ultimatum game, and the sequential common pool resource dilemma (CPR) game. Notably, the cooperation and fairness observed in the studied games are accounted for without adding an other-regarding component in the players’ utility functions. For the standard ultimatum game, the theory predicts a division of φ and 1 − φ, for the proposer and responder, respectively, where φ is the famous Golden Ratio (≈0.618), most known for its aesthetically pleasing properties. We discuss possible extensions of the proposed theory to repeated and evolutionary ultimatum games.Games2017-01-0381Article10.3390/g801000222073-43362017-01-03doi: 10.3390/g8010002Ramzi Suleiman<![CDATA[Games, Vol. 7, Pages 40: Network Formation with Endogenous Link Strength and Decreasing Returns to Investment]]>
http://www.mdpi.com/2073-4336/7/4/40
We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the direct link between any pair of agents is a concave function of their investments towards each other. In comparison with some existing models of network formation where the strength technology is a convex function of investment, we find that (i) the symmetric complete network can dominate the star architecture in terms of total utility; (ii) a dominating symmetric complete network needs not be stable; and, (iii) star and complete networks can be dominated by small-world networks.Games2016-12-0874Article10.3390/g7040040402073-43362016-12-08doi: 10.3390/g7040040Chiu So<![CDATA[Games, Vol. 7, Pages 39: Modeling Poker Challenges by Evolutionary Game Theory]]>
http://www.mdpi.com/2073-4336/7/4/39
We introduce a model for studying the evolutionary dynamics of Poker. Notably, despite its wide diffusion and the raised scientific interest around it, Poker still represents an open challenge. Recent attempts for uncovering its real nature, based on statistical physics, showed that Poker in some conditions can be considered as a skill game. In addition, preliminary investigations reported a neat difference between tournaments and ‘cash game’ challenges, i.e., between the two main configurations for playing Poker. Notably, these previous models analyzed populations composed of rational and irrational agents, identifying in the former those that play Poker by using a mathematical strategy, while in the latter those playing randomly. Remarkably, tournaments require very few rational agents to make Poker a skill game, while ‘cash game’ may require several rational agents for not being classified as gambling. In addition, when the agent interactions are based on the ‘cash game’ configuration, the population shows an interesting bistable behavior that deserves further attention. In the proposed model, we aim to study the evolutionary dynamics of Poker by using the framework of Evolutionary Game Theory, in order to get further insights on its nature, and for better clarifying those points that remained open in the previous works (as the mentioned bistable behavior). In particular, we analyze the dynamics of an agent population composed of rational and irrational agents, that modify their behavior driven by two possible mechanisms: self-evaluation of the gained payoff, and social imitation. Results allow to identify a relation between the mechanisms for updating the agents’ behavior and the final equilibrium of the population. Moreover, the proposed model provides further details on the bistable behavior observed in the ‘cash game’ configuration.Games2016-12-0774Article10.3390/g7040039392073-43362016-12-07doi: 10.3390/g7040039Marco Javarone<![CDATA[Games, Vol. 7, Pages 38: Probabilistic Unawareness]]>
http://www.mdpi.com/2073-4336/7/4/38
The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands—modal and probabilistic—of doxastic logic.Games2016-11-3074Article10.3390/g7040038382073-43362016-11-30doi: 10.3390/g7040038Mikaël Cozic<![CDATA[Games, Vol. 7, Pages 37: Epistemically Robust Strategy Subsets]]>
http://www.mdpi.com/2073-4336/7/4/37
We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set Y i contains all player types that believe with sufficient probability that the others are of types in Y − i and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability.Games2016-11-2574Article10.3390/g7040037372073-43362016-11-25doi: 10.3390/g7040037Geir AsheimMark VoorneveldJörgen Weibull<![CDATA[Games, Vol. 7, Pages 36: Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals]]>
http://www.mdpi.com/2073-4336/7/4/36
This paper develops a game-theoretic and epistemic account of a peculiar mode of practical reasoning that sustains focal points but also more general forms of rule-following behavior which I call community-based reasoning (CBR). It emphasizes the importance of counterfactuals in strategic interactions. In particular, the existence of rules does not reduce to observable behavioral patterns but also encompasses a range of counterfactual beliefs and behaviors. This feature was already at the core of Wittgenstein’s philosophical account of rule-following. On this basis, I consider the possibility that CBR may provide a rational basis for cooperation in the prisoner’s dilemma.Games2016-11-1674Article10.3390/g7040036362073-43362016-11-16doi: 10.3390/g7040036Cyril Hédoin<![CDATA[Games, Vol. 7, Pages 35: Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium]]>
http://www.mdpi.com/2073-4336/7/4/35
In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno, 2016), the notion of PBE was used to provide a characterization of SE in terms of a strengthening of the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of “conservative” belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE.Games2016-11-1074Article10.3390/g7040035352073-43362016-11-10doi: 10.3390/g7040035Giacomo Bonanno<![CDATA[Games, Vol. 7, Pages 34: Coevolution of Cooperation and Layer Selection Strategy in Multiplex Networks]]>
http://www.mdpi.com/2073-4336/7/4/34
Recently, the emergent dynamics in multiplex networks, composed of layers of multiple networks, has been discussed extensively in network sciences. However, little is still known about whether and how the evolution of strategy for selecting a layer to participate in can contribute to the emergence of cooperative behaviors in multiplex networks of social interactions. To investigate these issues, we constructed a coevolutionary model of cooperation and layer selection strategies in which each an individual selects one layer from multiple layers of social networks and plays the Prisoner’s Dilemma with neighbors in the selected layer. We found that the proportion of cooperative strategies increased with increasing the number of layers regardless of the degree of dilemma, and this increase occurred due to a cyclic coevolution process of game strategies and layer selection strategies. We also showed that the heterogeneity of links among layers is a key factor for multiplex networks to facilitate the evolution of cooperation, and such positive effects on cooperation were observed regardless of the difference in the stochastic properties of network topologies.Games2016-11-0174Article10.3390/g7040034342073-43362016-11-01doi: 10.3390/g7040034Katsuki HayashiReiji SuzukiTakaya Arita<![CDATA[Games, Vol. 7, Pages 33: Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation]]>
http://www.mdpi.com/2073-4336/7/4/33
Who benefits from the ignorance of others? We address this question from the point of view of a policy maker who can induce some ignorance into a system of agents competing for resources. Evolutionary game theory shows that when unconditional cooperators or ignorant agents compete with defectors in two-strategy settings, unconditional cooperators get exploited and are rendered extinct. In contrast, conditional cooperators, by utilizing some kind of reciprocity, are able to survive and sustain cooperation when competing with defectors. We study how cooperation thrives in a three-strategy setting where there are unconditional cooperators, conditional cooperators and defectors. By means of simulation on various kinds of graphs, we show that conditional cooperators benefit from the existence of unconditional cooperators in the majority of cases. However, in worlds that make cooperation hard to evolve, defectors benefit.Games2016-10-2674Article10.3390/g7040033332073-43362016-10-26doi: 10.3390/g7040033Mike FarjamWladislaw MillMarian Panganiban<![CDATA[Games, Vol. 7, Pages 32: Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions]]>
http://www.mdpi.com/2073-4336/7/4/32
In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the “best informed player” would be sure to obtain if he/she were to sell the goods to his/her opponents via take-it-or-leave-it offers. Our mechanism is probabilistic and of an extensive form. It relies on a new solution concept, for analyzing extensive-form games of incomplete information, which assumes only mutual belief of rationality. Moreover, our mechanism enjoys several novel properties with respect to privacy, computation and collusion.Games2016-10-2674Article10.3390/g7040032322073-43362016-10-26doi: 10.3390/g7040032Jing ChenSilvio Micali<![CDATA[Games, Vol. 7, Pages 31: Evolutionary Inspection and Corruption Games]]>
http://www.mdpi.com/2073-4336/7/4/31
We extend a standard two-person, non-cooperative, non-zero sum, imperfect inspection game, considering a large population of interacting inspectees and a single inspector. Each inspectee adopts one strategy, within a finite/infinite bounded set of strategies returning increasingly illegal profits, including compliance. The inspectees may periodically update their strategies after randomly inter-comparing the obtained payoffs, setting their collective behaviour subject to evolutionary pressure. The inspector decides, at each update period, the optimum fraction of his/her renewable budget to invest on his/her interference with the inspectees’ collective effect. To deter the inspectees from violating, he/she assigns a fine to each illegal strategy. We formulate the game mathematically, study its dynamics and predict its evolution subject to two key controls, the inspection budget and the punishment fine. Introducing a simple linguistic twist, we also capture the corresponding version of a corruption game.Games2016-10-2474Article10.3390/g7040031312073-43362016-10-24doi: 10.3390/g7040031Stamatios KatsikasVassili KolokoltsovWei Yang<![CDATA[Games, Vol. 7, Pages 30: Simulating the Impact of Crossover Kidney Transplantation on the Nord Italia Transplant Program]]>
http://www.mdpi.com/2073-4336/7/4/30
The increasing number of patients affected by chronic kidney disease makes it necessary to rely on living donors. However, a patient often cannot exploit her potential donor, due to blood or tissue incompatibility. Therefore, crossover transplantation programs have been developed in several countriesin order to increase the number of people receiving a kidney from a living donor. After reviewing the essential medical facts needed for the subsequent results, we quickly introduce two known algorithms for crossover transplantation. Next, we consider a dataset provided by the Nord Italia Transplant program, and we apply the above algorithms in order to highlight the benefits of these efficient procedures.Games2016-10-2074Article10.3390/g7040030302073-43362016-10-20doi: 10.3390/g7040030Monica SalvioliRoberto LucchettiRosanna Torelli<![CDATA[Games, Vol. 7, Pages 29: What Goes Around, Comes Around: Experimental Evidence on Exposed Lies]]>
http://www.mdpi.com/2073-4336/7/4/29
We experimentally investigate the optimal way to handle the uncovering of a noble lie, that is, a lie that supposedly is in the best interest of a given community. For this purpose, we analyze a public good game with feedback to group members on the average contributions of the other group members. The computer program inflates the feedback and shows higher than real average contributions to the high contributors. As shown by earlier studies, the partial feedback inflation increases the total payoff of the public good as it avoids the feeling of being a sucker for above average contributors. The lie is then uncovered and we continue with different feedback modes on contributions, some inflated, some true. We find that players respond similarly to both feedback modes. However, with true feedback, initial contributions in the second stage are significantly higher than with inflated feedback.Games2016-10-2074Article10.3390/g7040029292073-43362016-10-20doi: 10.3390/g7040029Sarah MörtenhuberAndreas NicklischKai-Uwe Schnapp<![CDATA[Games, Vol. 7, Pages 28: When Do Types Induce the Same Belief Hierarchy?]]>
http://www.mdpi.com/2073-4336/7/4/28
Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.Games2016-10-0974Article10.3390/g7040028282073-43362016-10-09doi: 10.3390/g7040028Andrés PereaWillemien Kets<![CDATA[Games, Vol. 7, Pages 27: Evolution of Mindsight and Psychological Commitment among Strategically Interacting Agents]]>
http://www.mdpi.com/2073-4336/7/3/27
We study the evolution of strategic psychological capabilities in a population of interacting agents. Specifically, we consider agents which are either blind or with mindsight, and either transparent or opaque. An agent with mindsight can observe the psychological makeup of a transparent agent, i.e., its logic, emotions, commitments and other elements that determine how it chooses actions. A blind agent cannot observe and opaque agents cannot be observed. Our assumption that mindsight and transparency are costly and optional exposes a middle ground between standard game theory without mindsight and evolution of preferences theory with obligatory and costless mindsight. We show that the only evolutionarily stable monomorphic population is one in which all agents are blind, opaque, and act-rational. We find that mindsight, transparency, and rule-rational commitments may evolve, albeit only in a portion of the population that fluctuates in size over generations. We reexamine the Ultimatum and Trust games in light of our findings and demonstrate that an evolved population of agents can differ significantly from a population of simplistic payoff-maximizers in terms of psychological traits and economic outcomes.Games2016-09-2173Article10.3390/g7030027272073-43362016-09-21doi: 10.3390/g7030027Dimitry Rtischev<![CDATA[Games, Vol. 7, Pages 26: Evolutionary Game between Commensal and Pathogenic Microbes in Intestinal Microbiota]]>
http://www.mdpi.com/2073-4336/7/3/26
The human intestinal microbiota plays a fundamental role in host health and is associated with many diseases when the homeostasis is disturbed. Although recent achievements in metagenomic sequencing have begun to reveal the variety of microbial composition associated with healthy and disease states, species-specific interactions and systematic dynamics still pose a great challenge to resolve the complexity of human microbiota. Using Clostridium difficile infection in human intestinal microbiota as an example, we apply evolutionary game theory to gain a fundamental understanding of the phenotypic variability and dynamic progression of microbiota. Here, microbiota dynamics are determined by the frequency-dependent fitness of each phenotypic population in the presence of the others. More specifically, the fitness is a function of phenotypic composition of the microbiota. We show how the phenotypic variability of microbiota can be explained by game theoretical approach. Knowledge of this study provides a new perspective in administrating antibiotic when dealing with pathogenic invasion. Instead of solely targeting to pathogens, therapies should aim at the whole ecosystem by reducing the fitness of pathogens compared to that of commensal microbes. In this case, the system will eradicate the pathogens by itself.Games2016-09-1273Article10.3390/g7030026262073-43362016-09-12doi: 10.3390/g7030026Amy WuDavid Ross<![CDATA[Games, Vol. 7, Pages 25: Payoff Shares in Two-Player Contests]]>
http://www.mdpi.com/2073-4336/7/3/25
In imperfectly discriminating contests with symmetric valuations, equilibrium payoffs are positive shares of the value of the prize. In contrast to a bargaining situation, players’ shares sum to less than one because a residual share of the value is lost due to rent dissipation. In this paper, we consider contests with two players and investigate the relationship between these equilibrium shares and the parameters of a class of asymmetric Tullock contest success functions. Our main finding is that any players’ shares that sum up to less than one can arise as the unique outcome of a pure-strategy Nash equilibrium for appropriate parameters.Games2016-09-0973Article10.3390/g7030025252073-43362016-09-09doi: 10.3390/g7030025Samuel HäfnerGeorg Nöldeke<![CDATA[Games, Vol. 7, Pages 24: The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games]]>
http://www.mdpi.com/2073-4336/7/3/24
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system’s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.Games2016-09-0973Article10.3390/g7030024242073-43362016-09-09doi: 10.3390/g7030024Mauro MobiliaAlastair RucklidgeBartosz Szczesny<![CDATA[Games, Vol. 7, Pages 23: Trait Emotional Intelligence Is Related to Risk Taking when Adolescents Make Deliberative Decisions]]>
http://www.mdpi.com/2073-4336/7/3/23
Most forms of risky behavior reach their peak during adolescence. A prominent line of research is exploring the relationship between people’s emotional self-efficacy and risk taking, but little is known about this relationship in the cognitive-deliberative domain among adolescents. The main aim of the present study consists in investigating whether trait EI (Emotional Intelligence) is positively related to risk taking under predominantly cognitive-deliberative conditions among adolescents. Ninety-four adolescents played the cold version of the Columbia Card Task one month following an assessment of their trait EI. Results showed that trait EI is associated with risk taking under cognitive-deliberative conditions among adolescents. Moreover, the present research showed that trait EI is related to risk taking through the decision makers’ self-motivation. These results provide novel insights into research investigating the connections between emotional intelligence, decision science and adolescence research.Games2016-08-3173Article10.3390/g7030023232073-43362016-08-31doi: 10.3390/g7030023Angelo Panno<![CDATA[Games, Vol. 7, Pages 22: Auctions Versus Private Negotiations in Buyer-Seller Networks]]>
http://www.mdpi.com/2073-4336/7/3/22
Buyer-seller networks where price is determined by an ascending-bid auction are important in many economic examples such as certain real estate markets, radio spectrum sharing, and buyer-supplier networks. However, it may be that some sellers are better off not participating in the auction. We consider what happens if sellers can make a take it or leave it offer to one of their linked buyers before the auction takes place and thus such a seller can choose not to participate in the auction. We give conditions on the graph and buyers valuations under which the buyer and seller will both agree to such a take it or leave it offer. Specifically, the buyer-seller pair will choose private negotiation over the auction if the seller acts as a network bridge with power over the buyer and if there are enough buyers with low valuations so that the seller does not expect to receive a high price in the auction.Games2016-08-3173Article10.3390/g7030022222073-43362016-08-31doi: 10.3390/g7030022Alison Watts<![CDATA[Games, Vol. 7, Pages 21: Promoting Residential Recycling: An Alternative Policy Based on a Recycling Reward System]]>
http://www.mdpi.com/2073-4336/7/3/21
This paper analyzes a reward system that uses a club good to promote recycling. In particular, we examine a context of incomplete information in which the administrator is unable to observe the resident’s attitude towards recycling. The results suggest that despite the lack of information, the administrator is able to induce all types of residents to recycle when the reward is sufficiently high. Furthermore, we show that education programs, technologies that help to reduce the residential recycling cost and penalties for garbage dumping are complementary tools that could also promote recycling.Games2016-08-1773Article10.3390/g7030021212073-43362016-08-17doi: 10.3390/g7030021Tongzhe LiAna Espínola-ArredondoJill McCluskey<![CDATA[Games, Vol. 7, Pages 20: Space Debris Removal: A Game Theoretic Analysis]]>
http://www.mdpi.com/2073-4336/7/3/20
We analyse active space debris removal efforts from a strategic, game-theoretical perspective. Space debris is non-manoeuvrable, human-made objects orbiting Earth, which pose a significant threat to operational spacecraft. Active debris removal missions have been considered and investigated by different space agencies with the goal to protect valuable assets present in strategic orbital environments. An active debris removal mission is costly, but has a positive effect for all satellites in the same orbital band. This leads to a dilemma: each agency is faced with the choice between the individually costly action of debris removal, which has a positive impact on all players; or wait and hope that others jump in and do the ‘dirty’ work. The risk of the latter action is that, if everyone waits, the joint outcome will be catastrophic, leading to what in game theory is referred to as the ‘tragedy of the commons’. We introduce and thoroughly analyse this dilemma using empirical game theory and a space debris simulator. We consider two- and three-player settings, investigate the strategic properties and equilibria of the game and find that the cost/benefit ratio of debris removal strongly affects the game dynamics.Games2016-08-1173Article10.3390/g7030020202073-43362016-08-11doi: 10.3390/g7030020Richard KlimaDaan BloembergenRahul SavaniKarl TuylsDaniel HennesDario Izzo<![CDATA[Games, Vol. 7, Pages 19: Optimal Decision Rules in Repeated Games Where Players Infer an Opponent’s Mind via Simplified Belief Calculation]]>
http://www.mdpi.com/2073-4336/7/3/19
In strategic situations, humans infer the state of mind of others, e.g., emotions or intentions, adapting their behavior appropriately. Nonetheless, evolutionary studies of cooperation typically focus only on reaction norms, e.g., tit for tat, whereby individuals make their next decisions by only considering the observed outcome rather than focusing on their opponent’s state of mind. In this paper, we analyze repeated two-player games in which players explicitly infer their opponent’s unobservable state of mind. Using Markov decision processes, we investigate optimal decision rules and their performance in cooperation. The state-of-mind inference requires Bayesian belief calculations, which is computationally intensive. We therefore study two models in which players simplify these belief calculations. In Model 1, players adopt a heuristic to approximately infer their opponent’s state of mind, whereas in Model 2, players use information regarding their opponent’s previous state of mind, obtained from external evidence, e.g., emotional signals. We show that players in both models reach almost optimal behavior through commitment-like decision rules by which players are committed to selecting the same action regardless of their opponent’s behavior. These commitment-like decision rules can enhance or reduce cooperation depending on the opponent’s strategy.Games2016-07-2873Article10.3390/g7030019192073-43362016-07-28doi: 10.3390/g7030019Mitsuhiro NakamuraHisashi Ohtsuki<![CDATA[Games, Vol. 7, Pages 18: Sharing the Costs of Complex Water Projects: Application to the West Delta Water Conservation and Irrigation Rehabilitation Project, Egypt]]>
http://www.mdpi.com/2073-4336/7/3/18
Effective sharing mechanisms of joint costs among beneficiaries of a project are a fundamental requirement for the sustainability of the project. Projects that are heterogeneous both in terms of the landscape of the area under development or the participants (users) lead to a more complicated set of allocation mechanisms than homogeneous projects. The analysis presented in this paper uses cooperative game theory to develop schemes for sharing costs and revenues from a project involving various beneficiaries in an equitable and fair way. The proposed approach is applied to the West Delta irrigation project. It sketches a differential two-part tariff that reproduces the allocation of total project costs using the Shapley Value, a well-known cooperative game allocation solution. The proposed differential tariff, applied to each land section in the project reflecting their landscape-related costs, contrasts the unified tariff that was proposed using the traditional methods in the project planning documents.Games2016-07-1573Article10.3390/g7030018182073-43362016-07-15doi: 10.3390/g7030018Stefano MorettiFioravante PatroneAriel DinarSafwat Abdel-Dayem<![CDATA[Games, Vol. 7, Pages 17: Vertical Relationships within Platform Marketplaces]]>
http://www.mdpi.com/2073-4336/7/3/17
In two-sided markets a platform allows consumers and sellers to interact by creating sub-markets within the platform marketplace. For example, Amazon has sub-markets for all of the different product categories available on its site, and smartphones have sub-markets for different types of applications (gaming apps, weather apps, map apps, ridesharing apps, etc.). The network benefits between consumers and sellers depend on the mode of competition within the sub-markets: more competition between sellers lowers product prices, increases the surplus consumers receive from a sub-market, and makes platform membership more desirable for consumers. However, more competition also lowers profits for a seller which makes platform membership less desirable for a seller and reduces seller entry and the number of sub-markets available on the platform marketplace. This dynamic between seller competition within a sub-market and agents’ network benefits leads to platform pricing strategies, participation decisions by consumers and sellers, and welfare results that depend on the mode of competition. Thus, the sub-market structure is important when investigating platform marketplaces.Games2016-07-1273Article10.3390/g7030017172073-43362016-07-12doi: 10.3390/g7030017Mark Tremblay<![CDATA[Games, Vol. 7, Pages 16: Can We Predict the Winner in a Market with Network Effects? Competition in Cryptocurrency Market]]>
http://www.mdpi.com/2073-4336/7/3/16
We analyze how network effects affect competition in the nascent cryptocurrency market. We do so by examining early dynamics of exchange rates among different cryptocurrencies. While Bitcoin essentially dominates this market, our data suggest no evidence of a winner-take-all effect early in the market. Indeed, for a relatively long period, a few other cryptocurrencies competing with Bitcoin (the early industry leader) appreciated much more quickly than Bitcoin. The data in this period are consistent with the use of cryptocurrencies as financial assets (popularized by Bitcoin), and not consistent with winner-take-all dynamics. Toward the end of our sample, however, things change dramatically. Bitcoin appreciates against the USD, while other currencies depreciate against the USD. The data in this period are consistent with strong network effects and winner-take-all dynamics. This trend continues at the time of writing.Games2016-07-0773Article10.3390/g7030016162073-43362016-07-07doi: 10.3390/g7030016Neil GandalHanna Halaburda<![CDATA[Games, Vol. 7, Pages 15: Keeping Pace with Criminals: An Extended Study of Designing Patrol Allocation against Adaptive Opportunistic Criminals]]>
http://www.mdpi.com/2073-4336/7/3/15
Game theoretic approaches have recently been used to model the deterrence effect of patrol officers’ assignments on opportunistic crimes in urban areas. One major challenge in this domain is modeling the behavior of opportunistic criminals. Compared to strategic attackers (such as terrorists) who execute a well-laid out plan, opportunistic criminals are less strategic in planning attacks and more flexible in executing well-laid plans based on their knowledge of patrol officers’ assignments. In this paper, we aim to design an optimal police patrolling strategy against opportunistic criminals in urban areas. Our approach is comprised by two major parts: learning a model of the opportunistic criminal (and how he or she responds to patrols) and then planning optimal patrols against this learned model. The planning part, by using information about how criminals responds to patrols, takes into account the strategic game interaction between the police and criminals. In more detail, first, we propose two categories of models for modeling opportunistic crimes. The first category of models learns the relationship between defender strategy and crime distribution as a Markov chain. The second category of models represents the interaction of criminals and patrol officers as a Dynamic Bayesian Network (DBN) with the number of criminals as the unobserved hidden states. To this end, we: (i) apply standard algorithms, such as Expectation Maximization (EM), to learn the parameters of the DBN; (ii) modify the DBN representation that allows for a compact representation of the model, resulting in better learning accuracy and the increased speed of learning of the EM algorithm when used for the modified DBN. These modifications exploit the structure of the problem and use independence assumptions to factorize the large joint probability distributions. Next, we propose an iterative learning and planning mechanism that periodically updates the adversary model. We demonstrate the efficiency of our learning algorithms by applying them to a real dataset of criminal activity obtained from the police department of the University of Southern California (USC) situated in Los Angeles, CA, USA. We project a significant reduction in crime rate using our planning strategy as compared to the actual strategy deployed by the police department. We also demonstrate the improvement in crime prevention in simulation when we use our iterative planning and learning mechanism when compared to just learning once and planning. Finally, we introduce a web-based software for recommending patrol strategies, which is currently deployed at USC. In the near future, our learning and planning algorithm is planned to be integrated with this software. This work was done in collaboration with the police department of USC.Games2016-06-2773Article10.3390/g7030015152073-43362016-06-27doi: 10.3390/g7030015Chao ZhangShahrzad GholamiDebarun KarArunesh SinhaManish JainRipple GoyalMilind Tambe<![CDATA[Games, Vol. 7, Pages 14: Ergodic Inequality]]>
http://www.mdpi.com/2073-4336/7/3/14
Weak conditions are provided under which society’s long-run distribution of wealth is independent of initial asset holdings.Games2016-06-2473Discussion10.3390/g7030014142073-43362016-06-24doi: 10.3390/g7030014Thomas Norman<![CDATA[Games, Vol. 7, Pages 13: The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence]]>
http://www.mdpi.com/2073-4336/7/2/13
We investigate the role of framing, inequity in initial endowments and history in shaping behavior in a corrupt transaction by extending the one-shot bribery game introduced by Cameron et al. (2009) to a repeated game setting. We find that the use of loaded language significantly reduces the incidence of bribery and increases the level of punishment. Punishment of bribery leads to reduced bribery in future. The evidence suggests that this game captures essential features of a corrupt transaction, over and above any sentiments of inequity aversion or negative reciprocity However, showing subjects the history of past play has little effect on the level of corruption.Games2016-06-2272Article10.3390/g7020013132073-43362016-06-22doi: 10.3390/g7020013Ananish ChaudhuriTirnud PaichayontvijitErwann Sbai<![CDATA[Games, Vol. 7, Pages 12: Time-Preference Heterogeneity and Multiplicity of Equilibria in Two-Group Bargaining]]>
http://www.mdpi.com/2073-4336/7/2/12
We consider a multilateral bargaining game in which the agents can be classified into two groups according to their instantaneous preferences. In one of these groups there is one agent with a different discount factor. We analyze how this time-preference heterogeneity may generate multiplicity of equilibria. When such an agent is sufficiently more patient than the rest, there is an equilibrium in which her group-mates make the same proposal as the members of the other group. Thus, in heterogeneous groups the presence of more patient members may reduce the utility of its members.Games2016-05-1272Article10.3390/g7020012122073-43362016-05-12doi: 10.3390/g7020012Daniel CardonaAntoni Rubí-Barceló<![CDATA[Games, Vol. 7, Pages 11: Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games]]>
http://www.mdpi.com/2073-4336/7/2/11
Social motives are frequently used to explain deviations from selfishness in non-strategic settings such as the Dictator Game. Previous research has mainly focused on two-player games; the workings of social motives in multiplayer Dictator Games are less well understood. A core feature of multiplayer games is that players can consider inequalities between others, in addition to outcomes that have two-player analogues, such as social efficiency and the inequality between self and others. We expect that existing models of social motives can be improved if players are allowed to consider the inequality between others. Results from two laboratory experiments confirm this: motives for the inequality between others were found, and these motives could not be reduced to motives with dyadic analogues. Explorative analyses show that our findings are robust to a number of potential misspecifications: motives for the inequality between others were also found when utility included non-linear evaluations of inequality, and when alternative types of self-other comparison mechanisms were modeled. Thus, to adequately capture social motives in multiplayer games, models should account for the complexities of the multiplayer setting. We speculate that our findings also hold for strategic games; but further research is needed to elucidate this.Games2016-04-1272Article10.3390/g7020011112073-43362016-04-12doi: 10.3390/g7020011David MacroJeroen Weesie<![CDATA[Games, Vol. 7, Pages 10: Core Stability and Core Selection in a Decentralized Labor Matching Market]]>
http://www.mdpi.com/2073-4336/7/2/10
We propose a dynamic model of decentralized many-to-one matching in the context of a competitive labor market. Through wage offers and wage demands, firms compete over workers and workers compete over jobs. Firms make hire-and-fire decisions dependent on the wages of their own workers and on the alternative workers available on the job market. Workers bargain for better jobs; either individually or collectively as unions, adjusting wage demands upward/downward depending on whether they are currently employed/unemployed. We show that such a process is absorbed into the core with probability one in finite time. Moreover, within the core, allocations are selected that are characterized by surplus splitting according to a bargaining solution such that (i) firms and workforce share total revenue according to relative bargaining strengths, and (ii) workers receive equal workforce shares above their individual outside options. These results bridge empirical evidence and provide a rich set of testable predictions.Games2016-03-3072Article10.3390/g7020010102073-43362016-03-30doi: 10.3390/g7020010Heinrich NaxBary Pradelski<![CDATA[Games, Vol. 7, Pages 9: Climate Change and Market Collapse: A Model Applied to Darfur]]>
http://www.mdpi.com/2073-4336/7/1/9
A recurring argument in the global debate is that climate deterioration is likely to make social conflicts over diminishing natural resources more common in the future. The exact mechanism behind such a development has so far not been successfully characterized in the literature. In this paper, we present a general model of a community populated by farmers and herders who can either divide up land in a market economy or in autarky. The key insight from our model is that decreasing resources can make trade between the two groups collapse, which in turn makes each group’s welfare independent of that of the other. Predictions from the model are then applied to the conflict in Darfur. Our analysis suggests that three decades of drought in the area can at least partially explain the observed disintegration of markets and the subsequent rise of social tensions.Games2016-03-1871Article10.3390/g701000992073-43362016-03-18doi: 10.3390/g7010009Ola Olsson<![CDATA[Games, Vol. 7, Pages 8: The Impact of the Irrelevant: Temporary Buy-Options and Bidding Behavior in Auctions]]>
http://www.mdpi.com/2073-4336/7/1/8
With a laboratory experiment, we study the impact of buy-options and the corresponding buy-price on revenues and bidding behavior in (online) proxy-auctions with independent private valuations. We show that temporary buy-options may reduce revenues for two reasons: At low buy-prices, the application of the buy-option avoids revenue-enhancing bidding; at high buy-prices, bidders are reluctant to bid above the option price (even though the option is no longer available once an auction has started). The latter suggests a particular type of anchoring, where bidders use the buy-price to update their expectations about the strengths of their opponents.Games2016-03-0171Article10.3390/g701000882073-43362016-03-01doi: 10.3390/g7010008Ronald PeetersMartin StrobelDries VermeulenMarkus Walzl<![CDATA[Games, Vol. 7, Pages 7: Recent Advances in Experimental Studies of Social Dilemma Games]]>
http://www.mdpi.com/2073-4336/7/1/7
I provide a broad overview of the findings reported in the articles submitted for this special volume on experimental studies of social dilemma problems. I start by providing a synopsis of where current research stands on this topic. Then I go on to discuss the specific papers and how those papers extend our knowledge in this area and add value to the current state of the art.Games2016-02-2671Editorial10.3390/g701000772073-43362016-02-26doi: 10.3390/g7010007Ananish Chaudhuri<![CDATA[Games, Vol. 7, Pages 6: Acknowledgement to Reviewers of Games in 2015]]>
http://www.mdpi.com/2073-4336/7/1/6
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Games2016-02-0271Editorial10.3390/g701000662073-43362016-02-02doi: 10.3390/g7010006 Games Editorial Office<![CDATA[Games, Vol. 7, Pages 5: Revenue Implications of Strategic and External Auction Risk]]>
http://www.mdpi.com/2073-4336/7/1/5
Two experimental treatments are used to study the effects of auction risk across five mechanisms. The first canonical, baseline treatment features only strategic risk and replicates the standard results that overbidding relative to the risk neutral Nash equilibrium is prevalent in all common auction mechanisms except for the English auction. We do not find evidence that bidders’ measured risk preferences can explain these patterns of overbidding. To enhance salience, we introduce a second novel treatment with external risk. This treatment captures the risk, prevalent in online auctions, that winners will not receive a good of value. We find that dynamic auctions—including the English—are particularly susceptible to overbidding in this environment. We note that overbidding is somewhat diminished in later periods and that our results may thus have particular relevance for bidders who are not highly experienced or who have not directly experienced losses. We conclude with a brief discussion of research implications.Games2016-01-2771Article10.3390/g701000552073-43362016-01-27doi: 10.3390/g7010005Andrea RobbettMichael GrahamPeter Matthews<![CDATA[Games, Vol. 7, Pages 4: Pledges of Commitment and Cooperation in Partnerships]]>
http://www.mdpi.com/2073-4336/7/1/4
We use experimental methods to investigate whether pledges of commitment can improve cooperation in endogenously-formed partnerships facing a social dilemma. Treatments vary in terms of the individual’s: (1) opportunity to commit to their partner; (2) the cost of dissolving committed partnerships; and (3) the distribution of these dissolution costs between partners. Our findings show that pledges of commitment alone can increase cooperation and welfare in committed partnerships. The introduction of relatively large and equally split costs yields similar gains. In contrast, when costs to dissolve committed partnerships fall solely on the individual choosing to break up, pledges of commitment fail to improve cooperation and welfare.Games2016-01-2071Article10.3390/g701000442073-43362016-01-20doi: 10.3390/g7010004Lachlan DeerRalph-C. Bayer<![CDATA[Games, Vol. 7, Pages 3: Partner Selection and the Division of Surplus: Evidence from Ultimatum and Dictator Experiments]]>
http://www.mdpi.com/2073-4336/7/1/3
We study ultimatum and dictator environments with one-way, unenforceable pre-play communication from the proposer to the recipient, semantically framed as a promise. After observing this promise regarding how much the proposer will offer if selected, in our treatment conditions, recipients choose whether or not to select a particular proposer. We find that offers can increase in the ultimatum game both with non-competitive selection with a single potential proposer, and more so with competition, where the recipient chooses one of two potential proposers, as compared to the no selection baseline. Furthermore, the offer is rejected with higher probability if the promisemade by the selected proposer is higher than the eventual offer. Our dictator environment does not give the power to reject offers, thus selection power carries no benefits in the dictator game. Finally, independent of the game institution or proposer selection mechanism, promises provide credible signals for offers.Games2016-01-1971Article10.3390/g701000332073-43362016-01-19doi: 10.3390/g7010003Priyodorshi BanerjeeSujoy ChakravartySanmitra Ghosh<![CDATA[Games, Vol. 7, Pages 2: Malevolent Governance, Intra-Group Conflict and the Paradox of the Plenty: An Experiment]]>
http://www.mdpi.com/2073-4336/7/1/2
Using a laboratory experiment, we behaviourally study the impact of a sudden increase in the common-pool size on within-group conflict, i.e., the paradox of the plenty. We also consider the potential role of governance in avoiding this paradox. In the first stage, a randomly-chosen leader of the group determines how much of the common-pool resource to protect from second-stage conflict. In the next stage, each group member allocates his private endowment between working or fighting for a share of the unprotected resource. We consider two treatments: anarchy (consisting of the second stage only) and with a leader deciding in the first stage. We find that the existence of institutions is not always better than anarchy. This is aggravated when the resource size is higher. Group conflict (income) decreases (increases) only when leaders chose the strongest resource protection. When leaders are malevolent, i.e., they chose weak resource protection, outcomes are worse than when institutions are absent.Games2015-12-2971Article10.3390/g701000222073-43362015-12-29doi: 10.3390/g7010002Klarizze PuzonMarc Willinger<![CDATA[Games, Vol. 7, Pages 1: Double Blind Peer-Review in Games]]>
http://www.mdpi.com/2073-4336/7/1/1
Pre-publication peer-review forms the basis for how scholarly journals assess whether an articleis suitable for publication. [...]Games2015-12-2471Editorial10.3390/g701000112073-43362015-12-24doi: 10.3390/g7010001Ulrich BergerMartyn Rittman<![CDATA[Games, Vol. 6, Pages 677-684: Psychology of Game Playing: Introduction to a Special Issue]]>
http://www.mdpi.com/2073-4336/6/4/677
Game theory has focused attention on different problems at different times in its history. Currently, attention is devoted to investigating how human decision makers with bounded rationality choose strategies in interactive decisions. Behavioral economics, and more generally experimental games, have appeared in the literature with accelerating frequency since 1990, and this cannot continue indefinitely without a proportional expansion of journal space. This Special Issue includes contributions to behavioral economics, experimental games, and evolutionary game theory, using theoretical, experimental, and agent-based modeling techniques.Games2015-12-2164Editorial10.3390/g60406776776842073-43362015-12-21doi: 10.3390/g6040677Andrew ColmanBriony Pulford<![CDATA[Games, Vol. 6, Pages 637-676: Evidential Equilibria: Heuristics and Biases in Static Games of Complete Information]]>
http://www.mdpi.com/2073-4336/6/4/637
Standard equilibrium concepts in game theory find it difficult to explain the empirical evidence from a large number of static games, including the prisoners’ dilemma game, the hawk-dove game, voting games, public goods games and oligopoly games. Under uncertainty about what others will do in one-shot games, evidence suggests that people often use evidential reasoning (ER), i.e., they assign diagnostic significance to their own actions in forming beliefs about the actions of other like-minded players. This is best viewed as a heuristic or bias relative to the standard approach. We provide a formal theoretical framework that incorporates ER into static games by proposing evidential games and the relevant solution concept: evidential equilibrium (EE). We derive the relation between a Nash equilibrium and an EE. We illustrate these concepts in the context of the prisoners’ dilemma game.Games2015-11-1664Article10.3390/g60406376376762073-43362015-11-16doi: 10.3390/g6040637Ali al-NowaihiSanjit Dhami<![CDATA[Games, Vol. 6, Pages 604-636: The Role of Implicit Motives in Strategic Decision-Making: Computational Models of Motivated Learning and the Evolution of Motivated Agents]]>
http://www.mdpi.com/2073-4336/6/4/604
Individual behavioral differences in humans have been linked to measurable differences in their mental activities, including differences in their implicit motives. In humans, individual differences in the strength of motives such as power, achievement and affiliation have been shown to have a significant impact on behavior in social dilemma games and during other kinds of strategic interactions. This paper presents agent-based computational models of power-, achievement- and affiliation-motivated individuals engaged in game-play. The first model captures learning by motivated agents during strategic interactions. The second model captures the evolution of a society of motivated agents. It is demonstrated that misperception, when it is a result of motivation, causes agents with different motives to play a given game differently. When motivated agents who misperceive a game are present in a population, higher explicit payoff can result for the population as a whole. The implications of these results are discussed, both for modeling human behavior and for designing artificial agents with certain salient behavioral characteristics.Games2015-11-1264Article10.3390/g60406046046362073-43362015-11-12doi: 10.3390/g6040604Kathryn Merrick<![CDATA[Games, Vol. 6, Pages 588-603: The Role of the Decision-Making Regime on Cooperation in a Workgroup Social Dilemma: An Examination of Cyberloafing]]>
http://www.mdpi.com/2073-4336/6/4/588
A burgeoning problem facing organizations is the loss of workgroup productivity due to cyberloafing. The current paper examines how changes in the decision-making rights about what workgroup members can do on the job affect cyberloafing and subsequent work productivity. We compare two different types of decision-making regimes: autocratic decision-making and group voting. Using a laboratory experiment to simulate a data-entry organization, we find that, while autocratic decision-making and group voting regimes both curtail cyberloafing (by over 50%), it is only in group voting that there is a substantive improvement (of 38%) in a cyberloafer’s subsequent work performance. Unlike autocratic decision-making, group voting leads to workgroups outperforming the control condition where cyberloafing could not be stopped. Additionally, only in the group voting regime did production levels of cyberloafers and non-loafers converge over time.Games2015-11-0564Article10.3390/g60405885886032073-43362015-11-05doi: 10.3390/g6040588Brice CorgnetRoberto Hernán-GonzálezMatthew McCarter<![CDATA[Games, Vol. 6, Pages 574-587: Commitment to Cooperation and Peer Punishment: Its Evolution]]>
http://www.mdpi.com/2073-4336/6/4/574
Theoretical and empirical studies have generally weighed the effect of peer punishment and pool punishment for sanctioning free riders separately. However, these sanctioning mechanisms often pose a puzzling tradeoff between efficiency and stability in detecting and punishing free riders. Here, we combine the key aspects of these qualitatively different mechanisms in terms of evolutionary game theory. Based on the dilemmatic donation game, we introduce a strategy of commitment to both cooperation and peer punishment. To make the commitment credible, we assume that those willing to commit have to make a certain deposit. The deposit will be refunded as long as the committers faithfully cooperate in the donation game and punish free riders and non-committers. It turns out that the deposit-based commitment offers both the efficiency of peer punishment and the stability of pool punishment and that the replicator dynamics lead to transitions of different systems: pool punishment to commitment to peer punishment.Games2015-11-0364Article10.3390/g60405745745872073-43362015-11-03doi: 10.3390/g6040574Tatsuya SasakiIsamu OkadaSatoshi UchidaXiaojie Chen<![CDATA[Games, Vol. 6, Pages 560-573: Risk Aversion and Engagement in the Sharing Economy]]>
http://www.mdpi.com/2073-4336/6/4/560
The sharing economy is a new online community that has important implications for offline behavior. This study evaluates whether engagement in the sharing economy is associated with an actor’s aversion to risk. Using a web-based survey and a field experiment, we apply an adaptation of Holt and Laury’s (2002) risk lottery game to a representative sample of sharing economy participants. We find that frequency of activity in the sharing economy predicts risk aversion, but only in interaction with satisfaction. While greater satisfaction with sharing economy websites is associated with a decrease in risk aversion, greater frequency of usage is associated with greater risk aversion. This analysis shows the limitations of a static perspective on how risk attitudes relate to participation in the sharing economy.Games2015-10-2664Article10.3390/g60405605605732073-43362015-10-26doi: 10.3390/g6040560Jessica SantanaPaolo Parigi<![CDATA[Games, Vol. 6, Pages 521-559: Salience and Strategy Choice in 2 × 2 Games]]>
http://www.mdpi.com/2073-4336/6/4/521
We present a model of boundedly rational play in single-shot 2 × 2 games. Players choose strategies based on the perceived salience of their own payoffs and, if own-payoff salience is uninformative, on the perceived salience of their opponent’s payoffs. When own payoffs are salient, the model’s predictions correspond to those of Level-1 players in a cognitive hierarchy model. When it is the other player’s payoffs that are salient, the predictions of the model correspond to those of traditional game theory. The model provides unique predictions for the entire class of 2 × 2 games. It identifies games where a Nash equilibrium will always occur, ones where it will never occur, and ones where it will occur only for certain payoff values. It also predicts the outcome of games for which there are no pure Nash equilibria. Experimental results supporting these predictions are presented.Games2015-10-2364Article10.3390/g60405215215592073-43362015-10-23doi: 10.3390/g6040521Jonathan LelandMark Schneider<![CDATA[Games, Vol. 6, Pages 495-520: Names for Games: Locating 2 × 2 Games]]>
http://www.mdpi.com/2073-4336/6/4/495
Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing relationships and potential transformations between neighboring games. This article presents additional visualizations of the topology, and a naming system for locating all 2 × 2 games as combinations of game payoff patterns from the symmetric ordinal 2 × 2 games. The symmetric ordinal games act as coordinates locating games in maps of the payoff space of 2 × 2 games, including not only asymmetric ordinal games and the complete set of games with ties, but also ordinal and normalized equivalents of all games with ratio or real-value payoffs. An efficient nomenclature can contribute to a systematic understanding of the diversity of elementary social situations; clarify relationships between social dilemmas and other joint preference structures; identify interesting games; show potential solutions available through transforming incentives; catalog the variety of models of 2 × 2 strategic situations available for experimentation, simulation, and analysis; and facilitate cumulative and comparative research in game theory.Games2015-10-2264Article10.3390/g60404954955202073-43362015-10-22doi: 10.3390/g6040495Bryan Bruns<![CDATA[Games, Vol. 6, Pages 473-494: Reciprocity in Labor Market Relationships: Evidence from an Experiment across High-Income OECD Countries]]>
http://www.mdpi.com/2073-4336/6/4/473
We study differences in behavior across countries in a labor market context. To this end, we conducted a bilateral gift-exchange experiment comparing the behavior of subjects from five high-income OECD countries: Germany, Spain, Israel, Japan and the USA. We observe that in all countries, effort levels are increasing while rejection rates are decreasing in wage offers. However, we also find considerable differences in behavior across countries in both one-shot and repeated relationships, the most striking between Germany and Spain. We also discuss the influence of socio-economic indicators and the implications of our findings.Games2015-10-0964Article10.3390/g60404734734942073-43362015-10-09doi: 10.3390/g6040473Israel WaichmanCh’ng SiangTill RequateAric ShafranEva Camacho-CuenaYoshio IidaShosh Shahrabani<![CDATA[Games, Vol. 6, Pages 458-472: Cooperate without Looking in a Non-Repeated Game]]>
http://www.mdpi.com/2073-4336/6/4/458
We propose a simple model for why we have more trust in people who cooperate without calculating the associated costs. Intuitively, by not looking at the payoffs, people indicate that they will not be swayed by high temptations to defect, which makes them more attractive as interaction partners. We capture this intuition using a simple four-stage game. In the first stage, nature draws the costs and benefits of cooperation according to a commonly-known distribution. In the second stage, Player 1 chooses whether or not to look at the realized payoffs. In the third stage, Player 2 decides whether to exit or let Player 1 choose whether or not to cooperate in the fourth stage. Using backward induction, we provide a complete characterization for when we expect Player 1 to cooperate without looking. Moreover, we show with numerical simulations how cooperating without looking can emerge through simple evolutionary processes.Games2015-09-3064Article10.3390/g60404584584722073-43362015-09-30doi: 10.3390/g6040458Christian HilbeMoshe HoffmanMartin Nowak<![CDATA[Games, Vol. 6, Pages 438-457: Indirect Reciprocity with Optional Interactions and Private Information]]>
http://www.mdpi.com/2073-4336/6/4/438
We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright–Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio.Games2015-09-3064Article10.3390/g60404384384572073-43362015-09-30doi: 10.3390/g6040438Jason OlejarzWhan GhangMartin Nowak<![CDATA[Games, Vol. 6, Pages 413-437: Evolution of Decisions in Population Games with Sequentially Searching Individuals]]>
http://www.mdpi.com/2073-4336/6/4/413
In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game.Games2015-09-2964Article10.3390/g60404134134372073-43362015-09-29doi: 10.3390/g6040413Tadeas PriklopilKrishnendu Chatterjee<![CDATA[Games, Vol. 6, Pages 394-412: Framing and Feedback in Social Dilemmas with Partners and Strangers]]>
http://www.mdpi.com/2073-4336/6/4/394
We study framing effects in repeated social dilemmas by comparing payoff-equivalent Give- and Take-framed public goods games under varying matching mechanisms (Partners or Strangers) and levels of feedback (Aggregate or Individual). In the Give-framed game, players contribute to a public good, while in the Take-framed game, players take from an existing public good. The results show Take framing and Individual-level feedback lead to more extreme behavior (free-riding and full cooperation), especially for Partners. These results suggest Take framing and Individual-level feedback increase the variability of cooperation.Games2015-09-2564Article10.3390/g60403943944122073-43362015-09-25doi: 10.3390/g6040394Caleb CoxBrock Stoddard<![CDATA[Games, Vol. 6, Pages 381-393: Representing Others in a Public Good Game]]>
http://www.mdpi.com/2073-4336/6/3/381
In many important public good situations the decision-making power and authority is delegated to representatives who make binding decisions on behalf of a larger group. The purpose of this study is to compare contribution decisions made by individuals with contribution decisions made by group representatives. We present the results from a laboratory experiment that compares decisions made by individuals in inter-individual public good games with decisions made by representatives on behalf of their group in inter-group public good games. Our main finding is that contribution behavior differs between individuals and group representatives, but only for women. While men’s choices are equally self-interested as individuals and group representatives, women make less self-interested choices as group representatives.Games2015-09-2163Article10.3390/g60303813813932073-43362015-09-21doi: 10.3390/g6030381Karen HaugeOle Rogeberg<![CDATA[Games, Vol. 6, Pages 368-380: Alleviation and Sanctions in Social Dilemma Games]]>
http://www.mdpi.com/2073-4336/6/3/368
This paper reports an experiment which compares behaviour in two punishment regimes: (i) a standard public goods game with punishment in which subjects are given the opportunity to punish other group members (democratic punishment regime) and (ii) a public goods game environment where all group members exogenously experience an automatic reduction of their income (irrespective of their behaviour) and are given the opportunity to alleviate the automatic penalty (undemocratic punishment regime). We employ a within-subjects design where subjects experience both environments and control for order effects by alternating their sequence. Our findings indicate that average contributions and earnings in the undemocratic punishment environment are significantly lower relative to the standard public goods game with punishment. We also observe that in the undemocratic environment average contributions decay over time only when subjects have experienced the standard public goods game with punishment. As a result, alleviation is significantly less when subjects have experienced the standard public goods game with punishment compared to when they do not have such experience. However, the assignment of punishment is robust irrespective of the order in which the games are played.Games2015-09-2163Article10.3390/g60303683683802073-43362015-09-21doi: 10.3390/g6030368Michalis Drouvelis<![CDATA[Games, Vol. 6, Pages 347-367: Bargaining Mechanisms for One-Way Games]]>
http://www.mdpi.com/2073-4336/6/3/347
We introduce one-way games, a two-player framework whose distinguishable feature is that the private payoff of one (independent) player is determined only by her own strategy and does not depend on the actions taken by the other (dependent) player. We show that the equilibrium outcome in one-way games without side payments and the social cost of any ex post efficient mechanism can be far from the optimum. We also show that it is impossible to design a Bayes–Nash incentive-compatible mechanism for one-way games that is budget-balanced, individually rational and efficient. To address this negative result, we propose a privacy-preserving mechanism based on a single-offer bargaining made by the dependent player that leverages the intrinsic advantage of the independent player. In this setting the outside option of the dependent player is not known a priori; however, we show that the mechanism satisfies individual rationality conditions, is incentive-compatible, budget-balanced and produces an outcome that is more efficient than the equilibrium without payments. Finally, we show that a randomized multi-offer extension brings no additional benefit in terms of efficiency.Games2015-09-0863Article10.3390/g60303473473672073-43362015-09-08doi: 10.3390/g6030347Andrés AbeliukGerardo BerbegliaPascal Van Hentenryck<![CDATA[Games, Vol. 6, Pages 318-346: Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure]]>
http://www.mdpi.com/2073-4336/6/3/318
In this paper, we deduce a condition for a strategy S1 to be more abundant on average at equilibrium under weak selection than another strategy S2 in a population structured into a finite number of colonies of fixed proportions as the population size tends to infinity. It is assumed that one individual reproduces at a time with some probability depending on the payoff received in pairwise interactions within colonies and between colonies and that the offspring replaces one individual chosen at random in the colony into which the offspring migrates. It is shown that an expected weighted average equilibrium frequency of S1 under weak symmetric strategy mutation between S1 and S2 is increased by weak selection if an expected weighted payoff of S1 near neutrality exceeds the corresponding expected weighted payoff of S2. The weights are given in terms of reproductive values of individuals in the different colonies in the neutral model. This condition for S1 to be favoured by weak selection is obtained from a strong migration limit of the genealogical process under neutrality for a sample of individuals, which is proven using a two-time scale argument. The condition is applied to games between individuals in colonies with linear or cyclic dominance and between individuals belonging to groups represented by subsets of a given set.Games2015-09-0763Article10.3390/g60303183183462073-43362015-09-07doi: 10.3390/g6030318Dhaker KroumiSabin Lessard<![CDATA[Games, Vol. 6, Pages 299-317: Stable Sampling Equilibrium in Common Pool Resource Games]]>
http://www.mdpi.com/2073-4336/6/3/299
This paper reconsiders evidence from experimental common pool resource games from the perspective of a model of payoff sampling. Despite being parameter-free, the model is able to replicate some striking features of the data, including single-peaked frequency distributions, the persistent use of strictly dominated actionsand stable heterogeneity in choices. These properties can also be accurately replicated using logit quantal response equilibrium (QRE), but only by tuning the free parameter separately for separate games. When the QRE parameter is constrained to be the same across games, sampling equilibrium provides a superior fit to the data. We argue that these findings are likely to generalize to other complex games with multiple players and strategies.Games2015-08-3163Article10.3390/g60302992993172073-43362015-08-31doi: 10.3390/g6030299Juan CárdenasCésar MantillaRajiv Sethi<![CDATA[Games, Vol. 6, Pages 273-298: Bargaining over Strategies of Non-Cooperative Games]]>
http://www.mdpi.com/2073-4336/6/3/273
We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.Games2015-08-3163Article10.3390/g60302732732982073-43362015-08-31doi: 10.3390/g6030273Giuseppe AttanasiAurora García-GallegoNikolaos GeorgantzísAldo Montesano<![CDATA[Games, Vol. 6, Pages 262-272: Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation]]>
http://www.mdpi.com/2073-4336/6/3/262
Reciprocal cooperation can be studied in the Centipede game, in which two players alternate in choosing between a cooperative GO move and a non-cooperative STOP move. GO sustains the interaction and increases the player pair’s total payoff while incurring a small personal cost; STOP terminates the interaction with a favorable payoff to the defector. We investigated cooperation in four Centipede games differing in their payoffs at the game’s end (positive versus zero) and payoff difference between players (moderate versus high difference). The games shared the same game-theoretic solution, therefore they should have elicited identical decision patterns, according to orthodox game theory. Nevertheless, both zero-end payoffs and high payoff inequality were found to reduce cooperation significantly. Contrary to previous predictions, combining these two factors in one game resulted in a slight weakening of their independent deterrent effects. These findings show that small changes in the payoff function have large and significant effects on cooperation, and that the effects do not combine synergistically.Games2015-08-1863Article10.3390/g60302622622722073-43362015-08-18doi: 10.3390/g6030262Eva KrockowBriony PulfordAndrew Colman<![CDATA[Games, Vol. 6, Pages 251-261: Unfazed by Both the Bull and Bear: Strategic Exploration in Dynamic Environments]]>
http://www.mdpi.com/2073-4336/6/3/251
People in a changing environment must decide between exploiting options they currently favor and exploring alternative options that provide additional information about the state of the environment. For example, drivers must decide between purchasing gas at their currently favored station (i.e., exploit) or risk a fruitless trip to another station to evaluate whether the price has been lowered since the last visit. Previous laboratory studies on exploratory choice have found that people choose strategically and explore alternative options when it is more likely that the relative value of competing options has changed. Our study extends this work by considering how global trends (which affect all options equally) influence exploratory choice. For example, during an economic crisis, global gas prices may increase or decrease at all stations, yet consumers should still explore strategically to find the best option. Our research question is whether people can maintain effective exploration strategies in the presence of global trends that are irrelevant in that they do not affect the relative value of choice options. We find that people explore effectively irrespective of global trends.Games2015-08-1863Article10.3390/g60302512512612073-43362015-08-18doi: 10.3390/g6030251Peter RieferBradley Love<![CDATA[Games, Vol. 6, Pages 231-250: The Evolvability of Cooperation under Local and Non-Local Mutations]]>
http://www.mdpi.com/2073-4336/6/3/231
We study evolutionary dynamics in a population of individuals engaged in pairwise social interactions, encoded as iterated games. We consider evolution within the space of memory-1strategies, and we characterize all evolutionary robust outcomes, as well as their tendency to evolve under the evolutionary dynamics of the system. When mutations are restricted to be local, as opposed to non-local, then a wider range of evolutionary robust outcomes tend to emerge, but mutual cooperation is more difficult to evolve. When we further allow heritable mutations to the player’s investment level in each cooperative interaction, then co-evolution leads to changes in the payoff structure of the game itself and to specific pairings of robust games and strategies in the population. We discuss the implications of these results in the context of the genetic architectures that encode how an individual expresses its strategy or investment.Games2015-07-2363Article10.3390/g60302312312502073-43362015-07-23doi: 10.3390/g6030231Alexander StewartJoshua Plotkin<![CDATA[Games, Vol. 6, Pages 214-230: Fairness and Trust in Structured Populations]]>
http://www.mdpi.com/2073-4336/6/3/214
Classical economic theory assumes that people are rational and selfish, but behavioral experiments often point to inconsistent behavior, typically attributed to “other regarding preferences.” The Ultimatum Game, used to study fairness, and the Trust Game, used to study trust and trustworthiness, have been two of the most influential and well-studied examples of inconsistent behavior. Recently, evolutionary biologists have attempted to explain the evolution of such preferences using evolutionary game theoretic models. While deterministic evolutionary game theoretic models agree with the classical economics predictions, recent stochastic approaches that include uncertainty and the possibility of mistakes have been successful in accounting for both the evolution of fairness and the evolution of trust. Here I explore the role of population structure by generalizing and expanding these existing results to the case of non-random interactions. This is a natural extension since such interactions do not occur randomly in the daily lives of individuals. I find that, in the limit of weak selection, population structure increases the space of fair strategies that are selected for but it has little-to-no effect on the optimum strategy played in the Ultimatum Game. In the Trust Game, in the limit of weak selection, I find that some amount of trust and trustworthiness can evolve even in a well-mixed population; however, the optimal strategy, although trusting if the return on investment is sufficiently high, is never trustworthy. Population structure biases selection towards strategies that are both trusting and trustworthy trustworthy and reduces the critical return threshold, but, much like in the case of fairness, it does not affect the winning strategy. Further considering the effects of reputation and structure, I find that they act synergistically to promote the evolution of trustworthiness.Games2015-07-2063Article10.3390/g60302142142302073-43362015-07-20doi: 10.3390/g6030214Corina Tarnita<![CDATA[Games, Vol. 6, Pages 191-213: The Loser’s Bliss in Auctions with Price Externality]]>
http://www.mdpi.com/2073-4336/6/3/191
We consider auctions with price externality where all bidders derive utility from the winning price, such as charity auctions. In addition to the benefit to the winning bidder, all bidders obtain a benefit that is increasing in the winning price. Theory makes two predictions in such settings: First, individual bids will be increasing in the multiplier on the winning price. Second, individual bids will not depend on the number of other bidders. Empirically, we find no evidence that increasing the multiplier increases individual bids in a systematic way, but we find that increasing the number of bidders does. An analysis of individual bidding functions reveals that bidders underweight the incentives to win and overweight the incentives to lose.Games2015-07-0363Article10.3390/g60301911912132073-43362015-07-03doi: 10.3390/g6030191Ernan HaruvyPeter Popkowski Leszczyc<![CDATA[Games, Vol. 6, Pages 175-190: What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma]]>
http://www.mdpi.com/2073-4336/6/3/175
For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies.Games2015-06-2563Article10.3390/g60301751751902073-43362015-06-25doi: 10.3390/g6030175Ethan Akin<![CDATA[Games, Vol. 6, Pages 161-174: A Tale of Two Bargaining Solutions]]>
http://www.mdpi.com/2073-4336/6/2/161
We set up a rich bilateral bargaining model with four salient points (disagreement point, ideal point, reference point, and tempered aspirations point), where the disagreement point and the utility possibilities frontier are endogenously determined. This model allows us to compare two bargaining solutions that use reference points, the Gupta-Livne solution and the tempered aspirations solution, in terms of Pareto efficiency in a strategic framework. Our main result shows that the weights solutions place on the disagreement point do not directly imply a unique efficiency ranking in this bargaining problem with a reference point. In particular, the introduction of a reference point brings one more degree of freedom to the model which requires also the difference in the weights placed on the reference point to be considered in reaching an efficiency ranking.Games2015-06-1962Article10.3390/g60201611611742073-43362015-06-19doi: 10.3390/g6020161Emin KaragözoğluKerim Keskin<![CDATA[Games, Vol. 6, Pages 150-160: How Moral Codes Evolve in a Trust Game]]>
http://www.mdpi.com/2073-4336/6/2/150
This paper analyzes the dynamic stability of moral codes in a two population trust game. Guided by a moral code, members of one population, the Trustors, are willing to punish members of the other population, the Trustees, who defect. Under replicator dynamics, adherence to the moral code has unstable oscillations around an interior Nash Equilibrium (NE), but under smoothed best response dynamics we obtain convergence to Quantal Response Equilibrium (QRE).Games2015-06-0362Article10.3390/g60201501501602073-43362015-06-03doi: 10.3390/g6020150Jean RabanalDaniel Friedman<![CDATA[Games, Vol. 6, Pages 124-149: Should Law Keep Pace with Society? Relative Update Rates Determine the Co-Evolution of Institutional Punishment and Citizen Contributions to Public Goods]]>
http://www.mdpi.com/2073-4336/6/2/124
Until recently, theorists considering the evolution of human cooperation have paid little attention to institutional punishment, a defining feature of large-scale human societies. Compared to individually-administered punishment, institutional punishment offers a unique potential advantage: the ability to control how quickly legal rules of punishment evolve relative to social behavior that legal punishment regulates. However, at what rate should legal rules evolve relative to society to maximize compliance? We investigate this question by modeling the co-evolution of law and cooperation in a public goods game with centralized punishment. We vary the rate at which States update their legal punishment strategy relative to Citizens’ updating of their contribution strategy and observe the effect on Citizen cooperation. We find that when States have unlimited resources, slower State updating lead to more Citizen cooperation: by updating more slowly, States force Citizens to adapt to the legal punishment rules. When States depend on Citizens to finance their punishment activities, however, we find evidence of a ‘Goldilocks’ effect: optimal compliance is achieved when legal rules evolve at a critical evolutionary rate that is slow enough to force citizens to adapt, but fast enough to enable states to quickly respond to outbreaks of citizen lawlessness.Games2015-06-0362Article10.3390/g60201241241492073-43362015-06-03doi: 10.3390/g6020124Daria RoithmayrAlexander IsakovDavid Rand<![CDATA[Games, Vol. 6, Pages 79-123: Students, Temporary Workers and Co-Op Workers: An Experimental Investigation on Social Preferences]]>
http://www.mdpi.com/2073-4336/6/2/79
We conduct an artefactual field experiment to compare the individual preferences and propensity to cooperate of three pools of subjects: Undergraduate students, temporary workers and permanent workers. We find that students are more selfish and contribute less than workers. Temporary and permanent contract workers have similar other-regarding preferences and display analogous contribution patterns in an anonymous Public Good Game.Games2015-05-1862Article10.3390/g6020079791232073-43362015-05-18doi: 10.3390/g6020079Davide DragoneFabio GaleottiRaimondello Orsini<![CDATA[Games, Vol. 6, Pages 57-78: On the Three-Person Game Baccara Banque]]>
http://www.mdpi.com/2073-4336/6/2/57
Baccara banque is a three-person zero-sum game parameterized by \(\theta\in(0,1)\). A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium. However, this solution exists only for certain \(\theta\). A third solution, which we call the correlated cooperative equilibrium, always exists. Under a ''with replacement'' assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all \(\theta\).Games2015-05-0862Article10.3390/g602005757782073-43362015-05-08doi: 10.3390/g6020057Stewart EthierJiyeon Lee<![CDATA[Games, Vol. 6, Pages 39-56: A Model of Protocoalition Bargaining with Breakdown Probability]]>
http://www.mdpi.com/2073-4336/6/2/39
This paper analyses a model of legislative bargaining in which parties form tentative coalitions (protocoalitions) before deciding on the allocation of a resource. Protocoalitions may fail to reach an agreement, in which case they may be dissolved (breakdown) and a new protocoalition may form. We show that agreement is immediate in equilibrium, and the proposer advantage disappears as the breakdown probability goes to zero. We then turn to the special case of apex games and explore the consequences of varying the probabilities that govern the selection of formateurs and proposers. Letting the breakdown probability go to zero, most of the probabilities considered lead to the same ex post pay-off division. Ex ante expected pay-offs may follow a counterintuitive pattern: as the bargaining power of weak players within a protocoalition increases, the weak players may expect a lower pay-off ex ante.Games2015-04-2262Article10.3390/g602003939562073-43362015-04-22doi: 10.3390/g6020039Maria Montero<![CDATA[Games, Vol. 6, Pages 32-38: From Bargaining Solutions to Claims Rules: A Proportional Approach]]>
http://www.mdpi.com/2073-4336/6/1/32
Agents involved in a conflicting claims problem may be concerned with the proportion of their claims that is satisfied, or with the total amount they get. In order to relate both perspectives, we associate to each conflicting claims problem a bargaining-in-proportions set. Then, we obtain a correspondence between classical bargaining solutions and usual claims rules. In particular, we show that the constrained equal losses, the truncated constrained equal losses and the contested garment (Babylonian Talmud) rules can be obtained throughout the Nash bargaining solution.Games2015-03-0561Article10.3390/g601003232382073-43362015-03-05doi: 10.3390/g6010032José-Manuel Giménez-GómezAntónio OsórioJosep Peris<![CDATA[Games, Vol. 6, Pages 2-31: Selection-Mutation Dynamics of Signaling Games]]>
http://www.mdpi.com/2073-4336/6/1/2
We study the structure of the rest points of signaling games and their dynamic behavior under selection-mutation dynamics by taking the case of three signals as our canonical example. Many rest points of the replicator dynamics of signaling games are not isolated and, therefore, not robust under perturbations. However, some of them attract open sets of initial conditions. We prove the existence of certain rest points of the selection-mutation dynamics close to Nash equilibria of the signaling game and show that all but the perturbed rest points close to strict Nash equilibria are dynamically unstable. This is an important result for the evolution of signaling behavior, since it shows that the second-order forces that are governed by mutation can increase the chances of successful signaling.Games2015-01-0961Article10.3390/g60100022312073-43362015-01-09doi: 10.3390/g6010002Josef HofbauerSimon Huttegger<![CDATA[Games, Vol. 6, Pages 1: Acknowledgement to Reviewers of Games in 2014]]>
http://www.mdpi.com/2073-4336/6/1/1
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2014:[...]Games2015-01-0761Editorial10.3390/g6010001112073-43362015-01-07doi: 10.3390/g6010001 Games Editorial Office<![CDATA[Games, Vol. 5, Pages 234-256: Conditional Cooperation and the Marginal per Capita Return in Public Good Games]]>
http://www.mdpi.com/2073-4336/5/4/234
We investigate experimentally whether the extent of conditional cooperation in public good games depends on the marginal per capita return (MPCR) to the public good and type of game. The MPCR is varied from 0.2 to 0.4 to 0.8. The ‘standard’ game, in which three players contribute before a follower, is compared with a leader-follower game, in which one player leads and three follow. Even though we observe less conditional cooperation for an MPCR of 0.2, the prevalence of conditional cooperation remains relatively stable to changes in the MPCR and game timing. In contrast, the level of MPCR has a strong effect on unconditional contributions. Our results highlight the critical role played by leaders in a public good game.Games2014-11-1454Article10.3390/g50402342342562073-43362014-11-14doi: 10.3390/g5040234Edward CartwrightDenise Lovett<![CDATA[Games, Vol. 5, Pages 204-233: Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences]]>
http://www.mdpi.com/2073-4336/5/4/204
This paper attacks a problem like the one addressed in an earlier work (Potthoff, 2013) but is more mathematical. The setting is one where an election is to choose a single winner from m (&gt; 2) candidates, it is postulated that voters have knowledge of the preference profile of the electorate, and preference cycles are limited. Both papers devise voting systems whose two key goals are to select a Condorcet winner (if one exists) and to resist manipulation. These systems entail equilibrium strategies where everyone votes sincerely, no group of voters sharing the same preference ordering can gain by deviating given that no one else deviates, and the Condorcet candidate wins. The present paper uses two unusual ballot types. One asks voters to rank the candidates with respect both to their own preferences and to their discerned order of preference of the entire electorate. The other just asks voters for their own preference ranks plus approval votes. Novel mathematical elements distinguish this paper. Its Condorcet completion methods examine all candidate triples, sometimes analyze loop(s) of some of those triples, and order candidates in a set by first determining the last-place candidate. Its non-manipulability proofs involve mathematical induction on m.Games2014-10-3054Article10.3390/g50402042042332073-43362014-10-30doi: 10.3390/g5040204Richard Potthoff<![CDATA[Games, Vol. 5, Pages 191-203: A Note on the Core of TU-cooperative Games with Multiple Membership Externalities]]>
http://www.mdpi.com/2073-4336/5/4/191
A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.Games2014-10-2154Article10.3390/g50401911912032073-43362014-10-21doi: 10.3390/g5040191Heinrich Nax<![CDATA[Games, Vol. 5, Pages 188-190: Special Issue: Aspects of Game Theory and Institutional Economics]]>
http://www.mdpi.com/2073-4336/5/3/188
Classical economists from Adam Smith to Thomas Malthus and to Karl Marx have considered the importance of direct interdependence and direct interactions for the economy. This was even more the case for original institutionalist thinkers such as Thorstein Veblen, John Commons, and Clarence Ayres. In their writings, direct interdependence, interactions (or transactions) among agents, with all beneficial and with all problematic consequences, took center stage in economic analysis. Why, for instance, do people adhere to a particular new fashion or trend? Because others do, after eminent people, wealthy people, the “leisure class” (T. Veblen), have made it a symbol for status. The new fashion, however, ceases to serve as such a symbol once too many people follow it. The constant effort put into following trends and adopting fashion turns out to be a social dilemma, driven by Veblenian instincts, such as invidious distinction in predatory societies, conspicuous consumption and emulation. [...]Games2014-09-0453Editorial10.3390/g50301881881902073-43362014-09-04doi: 10.3390/g5030188Wolfram ElsnerTorsten HeinrichHenning SchwardtClaudius Gräbner<![CDATA[Games, Vol. 5, Pages 160-187: An Agent-Based Model of Institutional Life-Cycles]]>
http://www.mdpi.com/2073-4336/5/3/160
We use an agent-based model to investigate the interdependent dynamics between individual agency and emergent socioeconomic structure, leading to institutional change in a generic way. Our model simulates the emergence and exit of institutional units, understood as generic governed social structures. We show how endogenized trust and exogenously given leader authority influences institutional change, i.e., diversity in institutional life-cycles. It turns out that these governed institutions (de)structure in cyclical patterns dependent on the overall evolution of trust in the artificial society, while at the same time, influencing this evolution by supporting social learning. Simulation results indicate three scenarios of institutional life-cycles. Institutions may, (1) build up very fast and freeze the artificial society in a stable but fearful pattern (ordered system); (2) exist only for a short time, leading to a very trusty society (highly fluctuating system); and (3) structure in cyclical patterns over time and support social learning due to cumulative causation of societal trust (complex system).Games2014-08-1853Article10.3390/g50301601601872073-43362014-08-18doi: 10.3390/g5030160Manuel WäckerleBernhard RengsWolfgang Radax<![CDATA[Games, Vol. 5, Pages 140-159: Learning in Networks—An Experimental Study Using Stationary Concepts]]>
http://www.mdpi.com/2073-4336/5/3/140
Our study analyzes theories of learning for strategic interactions in networks. Participants played two of the 2 × 2 games used by Selten and Chmura [1]. Every participant played against four neighbors. As a distinct aspect our experimental design allows players to choose different strategies against each different neighbor. The games were played in two network structures: a lattice and a circle. We analyze our results with respect to three aspects. We first compare our results with the predictions of five different equilibrium concepts (Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium) which represent the long-run equilibrium of a learning process. Secondly, we relate our results to four different learning models (impulse-matching learning, action-sampling learning, self-tuning EWA, and reinforcement learning) which are based on the (behavioral) round-by-round learning process. At last, we compare the data with the experimental results of Selten and Chmura [1]. One main result is that the majority of players choose the same strategy against each neighbor. As other results, we observe an order of predictive success for the equilibrium concepts that is different from the order shown by Selten and Chmura and an order of predictive success for the learning models that is only slightly different from the order shown in a recent paper by Chmura, Goerg and Selten [2].Games2014-07-3153Article10.3390/g50301401401592073-43362014-07-31doi: 10.3390/g5030140Siegfried BerninghausThomas NeumannBodo Vogt<![CDATA[Games, Vol. 5, Pages 127-139: The Seawall Bargaining Game]]>
http://www.mdpi.com/2073-4336/5/2/127
Agents located from downstream to upstream along an estuary and exposed to a flooding risk have to invest in facilities like a seawall (or dike). As the benefits of that local public good increase along the estuary, upstream agents have to bargain for monetary compensation with the most downstream agent in exchange for more protection effort. The paper analyses different bargaining protocols and determines the conditions under which agents are better off. The results show that upstream agents are involved in a chicken game when they have to bargain with the most downstream agent.Games2014-06-2452Article10.3390/g50201271271392073-43362014-06-24doi: 10.3390/g5020127Rémy DelilleJean-Christophe Pereau<![CDATA[Games, Vol. 5, Pages 116-126: Two-Dimensional Effort in Patent-Race Games and Rent-Seeking Contests: The Case of Telephony]]>
http://www.mdpi.com/2073-4336/5/2/116
Using the political-economic history of the development of telephony during the 1870s as a backdrop, this paper studies a two-player Tullock contest that includes both research effort (R&amp;D) and legal effort (i.e., rent-seeking effort). The two types of efforts complement each other and positively influence the payoff of the contest. We assume that legal effort affects the prize value, increasing the winner’s prospective rents, and research effort impacts the probability of winning the contest. The results of the model break new ground in showing that research effort is a function of legal effort, wherein research effort increases with rent-seeking effort. The model also shows the existence of a strategic equivalence between rent seeking and patent races.Games2014-05-2052Article10.3390/g50201161161262073-43362014-05-20doi: 10.3390/g5020116João FariaFranklin Mixon, Jr.Steven CaudillSamantha Wineke<![CDATA[Games, Vol. 5, Pages 97-115: Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities]]>
http://www.mdpi.com/2073-4336/5/2/97
We characterize the efficiency space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto-optimal combinatorial auctions in a model with two players and k nonidentical items. We examine a model with multidimensional types, private values and quasilinear preferences for the players with one relaxation: one of the players is subject to a publicly known budget constraint. We show that if it is publicly known that the valuation for the largest bundle is less than the budget for at least one of the players, then Vickrey-Clarke-Groves (VCG) uniquely fulfills the basic properties of being deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal. Our characterization of the efficient space for deterministic budget constrained combinatorial auctions is similar in spirit to that of Maskin 2000 for Bayesian single-item constrained efficiency auctions and comparable with Ausubel and Milgrom 2002 for non-constrained combinatorial auctions.Games2014-04-3052Article10.3390/g5020097971152073-43362014-04-30doi: 10.3390/g5020097Anat LernerRica Gonen<![CDATA[Games, Vol. 5, Pages 92-96: Sequential Rationality in Continuous No-Limit Poker]]>
http://www.mdpi.com/2073-4336/5/2/92
Newman’s (1959, Operations Research, 7, 557–560) solution for a variant of poker with continuous hand spaces and an unlimited bet size is modified to incorporate sequential rationality.Games2014-04-1452Short Note10.3390/g502009292962073-43362014-04-14doi: 10.3390/g5020092Thomas Norman<![CDATA[Games, Vol. 5, Pages 90-91: Acknowledgement to Reviewers of Games in 2013]]>
http://www.mdpi.com/2073-4336/5/1/90
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013. [...]Games2014-02-2551Editorial10.3390/g501009090912073-43362014-02-25doi: 10.3390/g5010090 Games Editorial Office<![CDATA[Games, Vol. 5, Pages 53-89: Schelling, von Neumann, and the Event that Didn’t Occur]]>
http://www.mdpi.com/2073-4336/5/1/53
Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper.Games2014-02-2551Article10.3390/g501005353892073-43362014-02-25doi: 10.3390/g5010053Alexander Field<![CDATA[Games, Vol. 5, Pages 26-52: Examining Monotonicity and Saliency Using Level-k Reasoning in a Voting Game]]>
http://www.mdpi.com/2073-4336/5/1/26
This paper presents an experiment that evaluates the effect of financial incentives and complexity in political science voting experiments. To evaluate the effect of complexity we adopt a level-k reasoning model concept. This model by Nagel [1] postulates that players might be of different types, each corresponding to the level of reasoning in which they engage. Furthermore, to postulate the effect of financial incentives on subjects’ choice, we used the Quantal Response Equilibrium (QRE) concept. In a QRE, players’ decisions are noisy, with the probability of playing a given strategy increasing in its expected payoff. Hence, the choice probability is a function of the magnitude of the financial incentives. Our results show that low complexity promotes the highest degree of level-k strategic reasoning in every payment treatment. Standard financial incentives are enough to induce equilibrium behavior, and the marginal effect of extra incentives on equilibrium behavior seems to be negligible. High complexity, instead, decreases the rate of convergence to equilibrium play. With a sufficiently high complexity, increasing payoff amounts does promote more strategic behavior in a significant manner. Our results show with complex voting games, higher financial incentives are required for the subjects to exert the effort needed to complete the task.Games2014-02-1451Article10.3390/g501002626522073-43362014-02-14doi: 10.3390/g5010026Anna BassiKenneth Williams<![CDATA[Games, Vol. 5, Pages 1-25: Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results]]>
http://www.mdpi.com/2073-4336/5/1/1
The paper presents an evolutionary model, based on the assumption that agents may revise their current strategies if they previously failed to attain the maximum level of potential payoffs. We offer three versions of this reflexive mechanism, each one of which describes a distinct type: spontaneous agents, rigid players, and ‘satisficers’. We use simulations to examine the performance of these types. Agents who change their strategies relatively easily tend to perform better in coordination games, but antagonistic games generally lead to more favorable outcomes if the individuals only change their strategies when disappointment from previous rounds surpasses some predefined threshold.Games2014-01-3051Article10.3390/g50100011252073-43362014-01-30doi: 10.3390/g5010001Tassos Patokos<![CDATA[Games, Vol. 4, Pages 776-794: Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study]]>
http://www.mdpi.com/2073-4336/4/4/776
In this paper, we claim that agents confronting with new interactive situations apply behavioral heuristics that drastically reduce the problem complexity either by neglecting the other players’ incentives, or by restricting attention to subsets of “salient” outcomes. We postulate that these heuristics are sensitive to the manipulation of those features that can be modified without altering the (Nash) equilibrium structure of the game. We call these features “descriptive”. We test experimentally the effect of these descriptive features on both choice behavior and cross-game similarity perception. Analysis of individual choices confirms our hypotheses, and suggests that non-equilibrium choices may derive from simplified mental models of the game structure, rather than from heterogeneous beliefs or limited iterative thinking. In addition, subjects tend to behave similarly in games sharing similar descriptive features, regardless of their strategic structure.Games2013-12-1844Article10.3390/g40407767767942073-43362013-12-18doi: 10.3390/g4040776Sibilla Di GuidaGiovanna Devetag<![CDATA[Games, Vol. 4, Pages 754-775: External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal?]]>
http://www.mdpi.com/2073-4336/4/4/754
Prompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival’s competition, either with the alliance or with the individual partners. We show that, while strong external pressure on both partners can cause Ally-Ally to become a Nash equilibrium for the two-player Prisoners’ Dilemma, weak or asymmetric pressure that plays on the partners’ differing objectives can undermine the alliance. As well as providing new insights into how allies should respond if the alliance is to continue, this also illustrates how a third party can most effectively cause the alliance to become unsustainable. We create a new game theoretic framework, adding value to existing theory and the practice of alliance formation and sustainability.Games2013-12-1044Article10.3390/g40407547547752073-43362013-12-10doi: 10.3390/g4040754Jane BinnerLeslie FletcherVassili KolokoltsovFrancesco Ciardiello<![CDATA[Games, Vol. 4, Pages 738-753: Auctioning the Right to Play Ultimatum Games and the Impact on Equilibrium Selection]]>
http://www.mdpi.com/2073-4336/4/4/738
We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equilibrium, and auction prices emerge supporting this equilibrium by the principle of forward induction. With random assignment, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. While Nash equilibria with low offers are observed, the subgame perfect Nash equilibrium never is.Games2013-11-2744Article10.3390/g40407387387532073-43362013-11-27doi: 10.3390/g4040738Jason ShachatJ. Swarthout<![CDATA[Games, Vol. 4, Pages 711-737: A Game-Theoretic Analysis of Baccara Chemin de Fer]]>
http://www.mdpi.com/2073-4336/4/4/711
Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 x 288 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only his own total, baccara is a 2 x 2484 matrix game, which was solved by Downton and Lockwood in 1975 for d = 1, 2, . . . , 8. Assuming that cards are dealt without replacement from a d-deck shoe and that each of Player and Banker sees the composition of his own two-card hand, baccara is a 25 x 2484 matrix game, which is solved herein for every positive integer d.Games2013-11-1844Article10.3390/g40407117117372073-43362013-11-18doi: 10.3390/g4040711Stewart EthierCarlos Gámez<![CDATA[Games, Vol. 4, Pages 690-710: The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings]]>
http://www.mdpi.com/2073-4336/4/4/690
We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices.Games2013-11-1844Article10.3390/g40406906907102073-43362013-11-18doi: 10.3390/g4040690Rica GonenAnat Lerner<![CDATA[Games, Vol. 4, Pages 670-689: The Optimality of Team Contracts]]>
http://www.mdpi.com/2073-4336/4/4/670
This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others’ effort levels and draft enforceable side-contracts on effort levels and realized returns. Standard constraints, resulting in incentive contracts, fail to ensure implementability, and we examine centralized collusion-proof contracts and decentralized team contracts, as well. We prove that the principal may restrict attention to team contracts whenever returns from the project satisfy a mild monotonicity condition.Games2013-11-1844Article10.3390/g40406706706892073-43362013-11-18doi: 10.3390/g4040670Mehmet BarloAyça Özdoğan