Abstract: This paper studies the co-evolution of networks and play in the context of finite population potential games. Action revision, link creation and link destruction are combined in a continuous-time Markov process. I derive the unique invariant distribution of this process in closed form, as well as the marginal distribution over action profiles and the conditional distribution over networks. It is shown that the equilibrium interaction topology is an inhomogeneous random graph. Furthermore, a characterization of the set of stochastically stable states is provided, generalizing existing results to models with endogenous interaction structures.
Abstract: Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co-evolutionary dynamics of networks and play. We study a co-evolutionary process of networks and play in settings where players have diverse preferences. In the class of potential games we provide a closed-form solution for the unique invariant distribution of this process. Based on this result we derive various asymptotic statistics generated by the co-evolutionary process. We give a complete characterization of the random graph model, and stochastically stable states in the small noise limit. Thereby we can select among action profiles and networks which appear jointly with non-vanishing frequency in the limit of small noise in the population. We further study stochastic stability in the limit of large player populations.
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Abstract: 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 providing general formulas for the stochastic potentials arising under noisy-best response dynamics. This is in turn achieved by transforming the stochastic stability analysis into an optimal control problem, which can be solved generally. 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.
This project builds on earlier work (Stochastic stability in binary choice coordination games) in which we show that noisy best-response dynamics, commonly used as myopic adjustment processes in population games, can be reduced to the problem of solving an optimal control problem. The aim of the project is to develop computational methods for equilibrium selection in games. Thereby we hope to shad light on classical questions in game theory: If a game theoretic model forces us to make ambigous predictions, which is the most persistent one?