Competing Conventions with Costly Information Acquisition

We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough

Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games

Evolutionary games and equilibrium selection

In dieser Dissertation werden mehrere Methoden zur Gleichgewichtsselektion f¨ur gewisse Klassen von Spielen studiert. Es wird untersucht, inwiefern diese Methoden zu ¨ahnlichen oder verschiedenen Resultaten f¨uhren. Die Dissertation besteht aus f¨unf Kapiteln. In Kapitel 1 werden die theoretischen Grundlagen einer Homotopiemethode entlang des Graphen der quantal response Gleichgewichte beschrieben. In Kapitel 2 wird diese Methodik im Detail auf 2 × 2 Bimatrixspiele angewendet. Kapitel 3 untersucht das Ultimatumspiel mittels eines Lern- und Mutationsprozesses. Kapitel 4 widmet sich zwei weiteren Methoden der Gleichgewichtsauswahl, die auf der Replikatorgleichung basieren. Kapitel 5 stellt ein ¨okonomisches Experiment vor, das zeigt, wie eine strafende Institution dem Problem der Trittbrettfahrer Herr werden kann.The object of this thesis is to study several equilibrium selection methods for certain classes of games and compare to what extent these selection methods lead to similar or different results. The thesis consists of five chapters. Chapter 1 describes a theoretical framework for equilibrium selection by tracing the graph of the quantal response equilibrium (QRE) correspondence. Chapter 2 analyzes the quantal response methods for equilibrium selection in detail for 2 × 2 bimatrix games. Chapter 3 investigates the ultimatum game by a learning-mutation process related to the quantal response equilibrium. Chapter 4 studies two equilibrium selection methods based on the replicator dynamics. Chapter 5 provides a economic experiment to show that social learning can lead to a spontaneously emerging social contract, based on a sanctioning institution to overcome the free rider problem

Stochastic stability in asymmetric binary choice coordination games

Staudigl M. Stochastic stability in asymmetric binary choice coordination games. Games and Economic Behavior. 2012;75(1):372-401.A recent literature in evolutionary game theory is devoted to the question of robust equilibrium selection under noisy best-response dynamics. In this paper we present a complete picture of equilibrium selection for asymmetric binary choice coordination games in the small noise limit. We achieve this by transforming the stochastic stability analysis into an optimal control problem, which can be solved analytically. This approach allows us to obtain precise and clean equilibrium selection results for all canonical noisy best-response dynamics which have been proposed so far in the literature, among which we find the best-response with mutations dynamics, the logit dynamics and the probit dynamics. (C) 2011 Elsevier Inc. All rights reserved