Games — Open Access Journal

I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games. Full article

We propose a dual selves model to integrate affective responses and belief-dependent emotions into game theory. We apply our model to team production and model a worker as being composed of a rational self, who chooses effort, and an emotional self, who expresses esteem. Similar to psychological game theory, utilities depend on beliefs, but only indirectly. More concretely, emotions affect utilities, and the expression of emotions depends on updated beliefs. Modeling affective responses as actions chosen by the emotional self allows us to apply standard game-theoretic solution concepts. The model reveals that with incomplete information about abilities, workers only choose high effort if esteem is expressed based on interpersonal comparisons and if the preference for esteem is a status preference. Full article

Game spaces in which an organism must repeatedly compete with an opponent for mutually exclusive outcomes are critical methodologies for understanding decision-making under pressure. In the non-transitive game rock, paper, scissors (RPS), the only technique that guarantees the lack of exploitation is to perform randomly in accordance with mixed-strategy. However, such behavior is thought to be outside bounded rationality and so decision-making can become deterministic, predictable, and ultimately exploitable. This review identifies similarities across economics, neuroscience, nonlinear dynamics, human, and animal cognition literatures, and provides a taxonomy of RPS strategy. RPS strategies are discussed in terms of (a) whether the relevant computations require sensitivity to item frequency, the cyclic relationships between responses, or the outcome of the previous trial, and (b) whether the strategy is framed around the self or other. The negative implication of this taxonomy is that despite the differences in cognitive economy and recursive thought, many of the identified strategies are behaviorally isomorphic. This makes it difficult to infer strategy from behavior. The positive implication is that this isomorphism can be used as a novel design feature in furthering our understanding of the attribution, agency, and acquisition of strategy in RPS and other game spaces. Full article

We study a model in which agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members via proportional sharing. We conduct an economic experiment using this model to investigate possible behavioral factors that may explain deviations from theoretical predictions. The main findings show that agents display rational behavior when forming coalitions, especially when they know that a large proportion of their opponents play myopic strategies from the outset. Over time, however, agents learn to behave more strategically and even more rationally, thus enabling agents to display more of the behavior predicted by the coalition formation model with farsighted agents. Full article

Solidarity in teamwork situations is important for the success and longevity of teams. This paper studies how helping group members is affected when groups are randomly merged and increase in size. Group mergers put social norms that are prevailing in previously small groups to the test as new team members may not share the same norms and values. I present results from an experiment in which subjects interact in groups and face the decision to help a group member who is in need of help due to an exogenous shock. Subjects interact in small groups in the first part of the experiment and groups are randomly merged to form big groups in the second part of the experiment. Helping rates are higher in merged groups compared with big groups that stay in the same constellation throughout the experiment. Moreover, in merged groups, high helping norms are more influential compared with low helping norms. Full article

Recent developments in information and communication technologies allow candidates for office to engage in sophisticated messaging strategies to influence voter choice. We consider how access to different technologies influence the choice of policy platforms by candidates. We find that when candidates can target messages to specific voter groups, platforms are more likely to be inefficient. In particular, when candidates can run targeted campaigns, they commit to projects that benefit small groups even when the social cost of these projects outweigh their benefits. Our results are robust to negative advertising. Full article

We investigate whether individuals’ self-stated privacy behavior is correlated with their reservation price for the disclosure of personal and potentially sensitive information. Our incentivized experiment has a unique setting: Information about choices with real implications could be immediately disclosed to an audience of fellow first semester students. Although we find a positive correlation between respondents’ willingness to accept (WTA) disclosure of their private information and their stated privacy behavior for some models, this correlation disappears when we change the specification of the privacy index. Independent of the privacy index chosen we find that the WTA is significantly influenced by individual responses to personal questions, as well as by different decisions to donate actual money, indicating that the willingness to protect private information depends on the delicacy of the information at stake. Full article

In most situations of voluntary contribution people are willing to give at the beginning, however contribution rates decay over time. In a new setup we introduce non-enforceable sharing rules, as requests, in a repeated redistribution game (called tip pooling). Three experimental treatments differ by the requested amount of sharing of privately known random endowments (tips), with one player never receiving any endowment. Using a hurdle model, we find no significant difference in free riding between the three sharing rules, but strong differences in positive contributions which, however, are lower than the rules prescribe. Furthermore, the average positive contribution remains stable over time, while free riding tends to increase. Full article

Ransomware is a particular form of cyber-attack in which a victim loses access to either his electronic device or files unless he pays a ransom to criminals. A criminal’s ability to make money from ransomware critically depends on victims believing that the criminal will honour ransom payments. In this paper we explore the extent to which a criminal can build trust through reputation. We demonstrate that there are situations in which it is optimal for the criminal to always return the files and situations in which it is not. We argue that the ability to build reputation will depend on how victims distinguish between different ransomware strands. If ransomware is to survive as a long term revenue source for criminals then they need to find ways of building a good reputation. Full article

Adopting the group turnout model of Herrera and Mattozzi, J. Eur. Econ. Assoc. 2010, 8, 838–871, we investigate direct democracy with supermajority rule and different preference intensities for two sides of a referendum: Reform versus status quo. Two parties spend money and effort to mobilize their voters. We characterize the set of pure strategy Nash equilibria. We investigate the optimal majority rule that maximizes voters’ welfare. Using an example, we show that the relationship between the optimal majority rule and the preference intensity is not monotonic—the optimal majority rule is initially decreasing and then increasing in the preference intensity of the status quo side. We also show that when the preference intensity of the status quo side is higher, the easiness to mobilize voters on the status quo side is lower, or the payoff that the reform party receives is higher, the optimal majority rule is more likely to be supermajority. Full article

This note provides simple derivations of the equilibrium conditions for different voting games with incomplete information. In the standard voting game à la Austen-Smith and Banks (1996), voters update their beliefs, and, conditional on their being pivotal, cast their votes. However, in voting games such as those of Ellis (2016) and Fabrizi, Lippert, Pan, and Ryan (2019), given a closed and convex set of priors, ambiguity-averse voters would select a prior from this set in a strategy-contingent manner. As a consequence, both the pivotal and non-pivotal events matter to voters when deciding their votes. In this note, I demonstrate that for ambiguous voting games the conditional probability of being pivotal alone is no longer sufficient to determine voters’ best responses. Full article

We consider the problem of efficient emission abatement in a multi polluter setting, where agents are located along a river in which net emissions accumulate and induce negative externalities to downstream riparians. Assuming a cooperative transferable utility game, we seek welfare distributions that satisfy all agents’ participation constraints and, in addition, a fairness constraint implying that no coalition of agents should be better off than it were if all non-members of the coalition would not pollute the river at all. We show that the downstream incremental distribution, as introduced by Ambec and Sprumont (2002), is the only welfare distribution satisfying both constraints. In addition, we show that this result holds true for numerous extensions of our model. Full article

An evolutionary model of European football was applied to analyze a two-stage indirect evolution game in which teams choose their utility function in the first stage, and their optimal talent investments in the second stage. Given the second-stage optimal aggregate-taking strategy (ATS) of talent investment, it was shown that teams may choose a mix of profit or win maximization as their objective, where the former is of considerably higher relevance with linear weights for profits, and is more successful in the utility function. With linear weights for profit and win maximization, maximizing profits is the only evolutionarily stable strategy (ESS) of teams. The results change if quadratic weights for profits and wins are employed. With increasing talent productivity, win maximization dominates in the static and in the dynamic versions of the model. As a consequence, it is an open question whether the commercialization of football (and other sports) leagues will lead to more profit or win maximization. Full article

We propose a new family of mechanisms, whereby players may give more or less directly to one another. A cornerstone case is the regular linear public goods mechanism (LPGM), where all contribute into a single common group account, the total amount of which is then distributed equally among players. We show that with sufficiently (yet not necessarily fully) pro-social preferences, the social optimum can be reached in Nash equilibrium in all social dilemma situations described by our mechanisms (including the LPGM). In addition, for a given heterogeneity of pro-social preferences, we help to identify which specific mechanisms perform best in terms of incentivizing giving. Our results are therefore relevant from two vantage points. One, they provide proper rational choice benchmarks based on Nash equilibrium under the assumption of other-regarding preferences. Two, they provide arguments in favor of re-structuring many collective action problems currently implemented as LPGMs when it is feasible to gain some information concerning who has concern for whom. Full article

We design an experiment to test how voters vote in a small committee election with three alternatives. Voters have common preferences that depend on an unknown state of nature. Each voter receives an imprecise private signal prior to the election and then casts a vote. The alternative with the most votes wins. We fix the number of voters in our experiment to be five and focus on differences in the information structure (prior and signal distributions). We test three different treatments (different prior and signal distributions) that pose different challenges for the voters. In one, simply voting for one’s signal is an equilibrium. In the other two, it is not. Despite the different levels of complexity for the voters, they come relatively close to the predicted strategies (that sometimes involve mixing). As a consequence, the efficiency of the decision is also relatively high and comes close to predicted levels. In one variation of the experiment, we calculate posterior beliefs for the subjects and post them. In another, we do not. Interestingly, the important findings do not change. Full article

Refinements of the Nash equilibrium have followed the strategy of extending the idea of subgame perfection to incomplete information games. This has been achieved by appropriately restricting beliefs at unreached information sets. Each new refinement gives stricter and more mathematically-complicated limitations on permitted beliefs. A simpler approach is taken here, where the whole idea of beliefs is dispensed with, and a new equilibrium concept, called the ideal reactive equilibrium, that builds on some pioneering work by Amershi, Sadanand and Sadanand on thought process dynamics, is developed. Full article

We make use of data from a Facebook application where hundreds of thousands of people played a simultaneous move, zero-sum game—rock-paper-scissors—with varying information to analyze whether play in strategic settings is consistent with extant theories. We report three main insights. First, we observe that most people employ strategies consistent with Nash, at least some of the time. Second, however, players strategically use information on previous play of their opponents, a non-Nash equilibrium behavior; they are more likely to do so when the expected payoffs for such actions increase. Third, experience matters: players with more experience use information on their opponents more effectively than less experienced players, and are more likely to win as a result. We also explore the degree to which the deviations from Nash predictions are consistent with various non-equilibrium models. We analyze both a level-k framework and an adapted quantal response model. The naive version of each these strategies—where players maximize the probability of winning without considering the probability of losing—does better than the standard formulation. While one set of people use strategies that resemble quantal response, there is another group of people who employ strategies that are close to $k_1$; for naive strategies the latter group is much larger. Full article

We consider the problem of sharing the cost of connecting a large number of atomless agents in a network. The centralized agency elicits the target nodes that agents want to connect, and charges agents based on their demands. We look for a cost-sharing mechanism that satisfies three desirable properties: efficiency which charges agents based on the minimum total cost of connecting them in a network, stand-alone core stability which requires charging agents not more than the cost of connecting by themselves directly, and limit routing-proofness which prevents agents from profitable reporting as several agents connecting from A to C to B instead of A to B. We show that these three properties are not always compatible for any set of cost functions and demands. However, when these properties are compatible, a new egalitarian mechanism is shown to satisfy them. When the properties are not compatible, we find a rule that meets stand-alone core stability, limit routing-proofness and minimizes the budget deficit. Full article

Individuals have a strong tendency to coordinate with all their neighbors on social and economics networks. Coordination is often influenced by intrinsic preferences among the available options, which drive people to associate with similar peers, i.e., homophily. Many studies reported that behind coordination game equilibria there is the individuals’ heterogeneity of preferences and that such heterogeneity is given a priori. We introduce a new mechanism which allows us to analyze the issue of heterogeneity from a cultural evolutionary point of view. Our framework considers agents interacting on a multiplex network who deal with coordination issues using social learning and payoff-driven dynamics. Agents form their heterogeneous preference through learning on one layer and they play a pure coordination game on the other layer. People learn from their peers that coordination is good and they also learn how to reach it either by conformism behavior or sorting strategy. We find that the presence of the social learning mechanism explains the rising and the endurance of a segregated society when members are diverse. Knowing how culture affects the ability to coordinate is useful for understanding how to reach social welfare in a diverse society. Full article