Inspired by Scarf, Zhao, Sandholm and Yang and Zhang, we introduce the model of coalitional population games with infinitely many pure strategies, and define the notions of NTU core and TU core for coalitional population games. We next prove the existence results for NTU cores and TU cores. Furthermore, as an extension of the NTU core, we introduce the notion of strong equilibria and prove the existence theorem of strong equilibria.

We study a class of two-player normal-form games with cyclical payoff structures. A game is called circulant if both players’ payoff matrices fulfill a rotational symmetry condition. The class of circulant games contains well-known examples such as Matching Pennies, Rock-Paper-Scissors, as well as subclasses of coordination and common interest games. The best response correspondences in circulant games induce a partition on each player’s set of pure strategies into equivalence classes. In any Nash Equilibrium, all strategies within one class are either (...) played with strictly positive or with zero probability. We further show that, strikingly, a single parameter fully determines the exact number and the structure of all Nash equilibria in these games. The parameter itself only depends on the position of the largest payoff in the first row of one of the player’s payoff matrix. (shrink)

This paper applies the theoretical criteria laid out by D’Arms et al. to various aspects of evolutionary models of signalling. The question that D’Arms et al. seek to answer can be formulated as follows: Are the models that we use to explain the phenomena in question conceptually adequate? The conceptual adequacy question relates the formal aspects of the model to those aspects of the natural world that the model is supposed to capture. Moreover, this paper extends the analysis of D’Arms (...) et al. by asking the following additional question: Are the models that we use sufficient to explain the phenomena in question? The sufficiency question asks what formal resources are minimally required for the model to get the right results most of the time. (shrink)

The origins of human social cooperation confound simple evolutionary explanation. But from Darwin and Durkheim onward, theorists (anthropologists and sociologists especially) have posited a potential link with another curious and distinctively human social trait that cries out for explanation: religion. This dissertation explores one contemporary theory of the co-evolution of religion and human social cooperation: the signalling theory of religion, or religious signalling theory (RST). According to the signalling theory, participation in social religion (and its associated rituals and sanctions) acts (...) as an honest signal of one’s commitment to a religiously demarcated community and its way of doing things. This signal would allow prosocial individuals to positively assort with one another for mutual advantage, to the exclusion of more exploitative individuals. In effect, the theory offers a way that religion and cooperation might explain one another, but which that stays within an individualist adaptive paradigm. My approach is not to assess the empirical adequacy of the religious signalling explanation or contrast it with other explanations, but rather to deal with the theory in its own terms – isolating and fleshing out its core commitments, explanatory potential, and limitations. The key to this is acknowledging the internal complexities of signalling theory, with respect to the available models of honest signalling and the extent of their fit (or otherwise) with religion as a target system. The method is to take seriously the findings of formal modelling in animal signalling and other disciplines, and to apply these (and methods from the philosophy of biology more generally) to progressively build up a comprehensive picture of the theory, its inherent strengths and weaknesses. The first two chapters outline the dual explanatory problems that cooperation and religion present for evolutionary human science, and surveys contemporary approaches toward explaining them. Chapter three articulates an evolutionary conception of the signalling theory, and chapters four to six make the case for a series of requirements, limitations, and principles of application. Chapters seven and eight argue for the value of formal modelling to further flesh out the theory’s commitments and potential and describe some simple simulation results which make progress in this regard. Though the inquiry often problematizes the signalling theory, it also shows that it should not be dismissed outright, and that it makes predictions which are apt for empirical testing. (shrink)

‘Noise’ in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested ‘what kind of noise’ is supported by behavioral evidence. This empirical analysis complements a growing theoretical literature on ‘how noise matters’ for equilibrium selection. We find that the vast majority of decisions constitute myopic best responses, but deviations continue to occur with probabilities that are sensitive to their costs, that is, (...) less frequent when implying larger payoff losses relative to the myopic best response. In addition, deviation rates vary with patterns of realized payoffs that are related to trial-and-error behavior. While there is little evidence that deviations are clustered in time or space, there is evidence of individual heterogeneity. (shrink)

I explore the evolution of strategies in an Augmented Stag Hunt game that adds a punishing strategy to the ordinary Stag Hunt strategies of cooperating, which aims for optimality, and defecting, which “plays it safe.” Cooperating weakly dominates punishing and defecting is the unique evolutionarily stable strategy. Nevertheless, for a wide class of Augmented Stag Hunts, polymorphic strategies combining punishing and cooperating collectively have greater attracting power for replicator dynamics than that of the ESS. The analysis here lends theoretical support (...) to the altruistic punishment hypothesis in the social sciences. (shrink)

It is generally thought that cognition evolved to help us navigate complex environments. Social interactions make up one part of a complex environment, and some have argued that social settings are crucial to the evolution of cognition. This article uses the methods of evolutionary game theory to investigate the effect of social interaction on the evolution of cognition broadly construed as strategic learning or plasticity. I delineate the conditions under which social interaction alone, apart from any additional external environmental variation, (...) can provide the selective pressure necessary for the initial evolution of learning. Furthermore, it is argued that in the context of social interactions we should notexpect traditional learners that ‘best-respond’ to dominate the population. Consequently, it may be important to consider non-traditional learners when modelling social evolution. 1 Introduction2 The Model3 Adapting to the Population3.1 Learning an equlibrium4 Adapting to Individuals4.1 Learning a best response and non-traditional learners5 Conclusion. (shrink)

Recently, philosophers have drawn on tools from game theory to explore behavior in Hobbes’ state of nature. I take a similar approach and argue the Lockean state of nature is best conceived of as a conflictual coordination game. I also discuss Nozick’s famous claim regarding the emergence of the state and argue the path to the minimal state is blocked by a hitherto unnoticed free-rider problem. Finally, I argue that on my representation of the Lockean state of nature both widespread (...) conflict and lasting peace are possible. This, I contend, is in line with one popular interpretation of Locke. (shrink)

Using results from evolutionary game theory, we analyze the conditions under which guilt can provide individual fitness benefits to actors, and so evolve. In particular, we focus on the individual benefits of guilty apology. We find that guilty apology is more likely to evolve in cases where actors interact repeatedly over long periods of time, where the costs of apology are low or moderate, and where guilt is hard to fake.

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich (...) the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

We identify a novel ‘cultural red king effect’ that, in many cases, results in stable arrangements which are to the detriment of minority groups. In particular, we show inequalities disadvantaging minority groups can naturally arise under an adaptive process when minority and majority members must routinely determine how to divide resources amongst themselves. We contend that these results show how inequalities disadvantaging minorities can likely arise by dint of their relative size and need not be a result of either explicit (...) nor implicit prejudices, nor due to intrinsic differences between minority and majority members. (shrink)

Game theory is often used to explain behavior. Such explanations often proceed by demonstrating that the behavior in question is a Nash equilibrium. Agents are in Nash equilibrium if each agent’s strategy maximizes her payoff given her opponents’ strategies. Nash equilibriums are fundamentally static, but it is usually assumed that equilibriums will be the outcome of a dynamic process of learning or evolution. This article demonstrates that, even in the most simple setting, this need not be true. In two-strategy games (...) with just a single equilibrium, a family of imitative learning dynamics does not lead to equilibrium. (shrink)

Cooperation in the prisoner’s dilemma is possible if interactions are sufficiently correlated. We show that when conditions favorable to the evolution of cooperation hold (rb > c) tag-based strategies dominate. Thus, well-meaning interventions aimed at promoting cooperation may succeed but will often lead to in-group favoritism and ethnocentric behavior. Exploring ways that promote cooperation but do not usher in tag-based strategies should be a focal point of future work on the evolution of cooperation.