Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

A population of agents recurrently plays a two-strategy population game. When an agent receives a revision opportunity, he chooses a new strategy using a noisy best response rule that satisfies mild regularity conditions; best response with mutations, logit choice, and probit choice are all permitted. We study the long run behavior of the resulting Markov process when the noise level $\eta$ is small and the population size $N$ is large. We obtain a precise characterization of the asymptotics of the stationary distributions $\mu^{N,\eta}$ as $\eta$ approaches zero and $N$ approaches infinity, and we establish that these asymptotics are the same for either order of limits and for all simultaneous limits. In general, different noisy best response rules can generate different stochastically stable states. To obtain a robust selection result, we introduce a refinement of risk dominance called \emph{stochastic dominance}, and we prove that coordination on a given strategy is stochastically stable under every noisy best response rule if and only if that strategy is stochastically dominant.Evolutionary game theory, stochastic stability, equilibrium selection

Essays on learning in games and social contexts

This dissertation studies the long-run outcome of learning in the prisoner's dilemma and in auctions as well as the occurrence of herds in social contexts

Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

Quantity Competition, Endogenous Motives and Behavioral Heterogeneity

The paper shows that strategic quantity competition can be characterized by behavioral heterogeneity, once competing firms are allowed in a pre-market stage to optimally choose the behavioral rule they will follow in their strategic choice of quantities. In particular, partitions of the population of identical firms in profit maximizers and relative profit maximizers turn out to be deviation-proof equilibria, both in simultaneous and sequential game structures. Our findings that in a strategic framework heterogeneous behavioral rules are consistent with individual incentives provides a game-theoretic microfoundation of heterogeneity.Behavioral Heterogeneity, Endogenous Motives, Relative Performance, Multistage Games, Quantity Competition.

Altruistic Learning

The origin of altruism remains one of the most enduring puzzles of human behaviour. Indeed, true altruism is often thought either not to exist, or to arise merely as a miscalculation of otherwise selfish behaviour. In this paper, we argue that altruism emerges directly from the way in which distinct human decision-making systems learn about rewards. Using insights provided by neurobiological accounts of human decision-making, we suggest that reinforcement learning in game-theoretic social interactions (habitisation over either individuals or games) and observational learning (either imitative of inference based) lead to altruistic behaviour. This arises not only as a result of computational efficiency in the face of processing complexity, but as a direct consequence of optimal inference in the face of uncertainty. Critically, we argue that the fact that evolutionary pressure acts not over the object of learning (‘what’ is learned), but over the learning systems themselves (‘how’ things are learned), enables the evolution of altruism despite the direct threat posed by free-riders

Learning in evolutionary environments

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Learning and evolution in games and oligopoly models

Dynamic models of adjustment, as well as static models of equilibrium, are important to understand economic reality. This thesis considers such dynamic models applied to economic games. The models can broadly be divided into two categories: learning and evolution. This thesis analyzes reinforcement learning and imitation dynamic on the learning side and the indirect evolution approach on the evolution side. It demonstrates the relation between the concept of Nash equilibrium and the long run outcome of the namic processes. The applications of the dynamic models to economic games include, among others, Cournot oligopoly and merger games.