Open AccessArticle
Anger Management: Aggression and Punishment in the Provision of Public Goods
Games 2017, 8(1), 5; doi:10.3390/g8010005 (registering DOI) -
Abstract
The ability to punish free-riders can increase the provision of public goods. However, sometimes, the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is
[...] Read more.
The ability to punish free-riders can increase the provision of public goods. However, sometimes, the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is that punishment can express anger about free-riding. If this is the case, then tools that regulate emotions could decrease the use of punishments while keeping welfare high, possibly depending on pre-existing levels of aggression. In this lab experiment, we find that adopting an objective attitude (objective), through a form of emotion regulation called cognitive reappraisal, decreases the use of punishments and makes a statistically insignificant improvement to both net earnings and self-reported emotions compared to a control condition (natural). Although the interaction between the emotion regulation treatment and level of aggression is not significant, only low aggression types reduce their punishments; the results are of the same direction, but statistically insignificant for high aggression types. Overall, our findings suggest that pairing emotion regulation with punishments can decrease the use of punishments without harming monetary and mental welfare. Full article
Figures

Figure 1

Open AccessArticle
The Evolution of Reputation-Based Cooperation in Regular Networks
Games 2017, 8(1), 8; doi:10.3390/g8010008 (registering DOI) -
Abstract
Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study
[...] Read more.
Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study of the interplay between both mechanisms remains almost uncharted. Here, we present a new individual-based model for the evolution of reciprocal cooperation between reputation and networks. We comparatively analyze four of the leading moral assessment rules—shunning, image scoring, stern judging, and simple standing—and base the model on the giving game in regular networks for Cooperators, Defectors, and Discriminators. Discriminators rely on a proper moral assessment rule. By using individual-based models, we show that the four assessment rules are differently characterized in terms of how cooperation evolves, depending on the benefit-to-cost ratio, the network-node degree, and the observation and error conditions. Our findings show that the most tolerant rule—simple standing—is the most robust among the four assessment rules in promoting cooperation in regular networks. Full article
Figures

Figure 1

Open AccessArticle
Social Pressure and Environmental Effects on Networks: A Path to Cooperation
Games 2017, 8(1), 7; doi:10.3390/g8010007 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessEditorial
Acknowledgement to Reviewers of Games in 2016
Games 2017, 8(1), 6; doi:10.3390/g8010006 -
Open AccessEditorial
A Nobel Prize for Property Rights Theory
Games 2017, 8(1), 4; doi:10.3390/g8010004 -
Abstract 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. Full article
Open AccessArticle
Economic Harmony: An Epistemic Theory of Economic Interactions
Games 2017, 8(1), 2; doi:10.3390/g8010002 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Cognitive Hierarchy Theory and Two-Person Games
Games 2017, 8(1), 1; doi:10.3390/g8010001 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies
Games 2017, 8(1), 3; doi:10.3390/g8010003 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Network Formation with Endogenous Link Strength and Decreasing Returns to Investment
Games 2016, 7(4), 40; doi:10.3390/g7040040 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Modeling Poker Challenges by Evolutionary Game Theory
Games 2016, 7(4), 39; doi:10.3390/g7040039 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Probabilistic Unawareness
Games 2016, 7(4), 38; doi:10.3390/g7040038 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Epistemically Robust Strategy Subsets
Games 2016, 7(4), 37; doi:10.3390/g7040037 -
Abstract
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
[...] Read more.
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 Yi contains all player types that believe with sufficient probability that the others are of types in Yi 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. Full article
Open AccessArticle
Community-Based Reasoning in Games: Salience, Rule-Following, and Counterfactuals
Games 2016, 7(4), 36; doi:10.3390/g7040036 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium
Games 2016, 7(4), 35; doi:10.3390/g7040035 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Coevolution of Cooperation and Layer Selection Strategy in Multiplex Networks
Games 2016, 7(4), 34; doi:10.3390/g7040034 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation
Games 2016, 7(4), 33; doi:10.3390/g7040033 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions
Games 2016, 7(4), 32; doi:10.3390/g7040032 -
Abstract
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
[...] Read more.
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. Full article
Open AccessArticle
Evolutionary Inspection and Corruption Games
Games 2016, 7(4), 31; doi:10.3390/g7040031 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
What Goes Around, Comes Around: Experimental Evidence on Exposed Lies
Games 2016, 7(4), 29; doi:10.3390/g7040029 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1

Open AccessArticle
Simulating the Impact of Crossover Kidney Transplantation on the Nord Italia Transplant Program
Games 2016, 7(4), 30; doi:10.3390/g7040030 -
Abstract
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
[...] Read more.
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. Full article
Figures

Figure 1