Research
Best-response Dynamics in Zero-sum Stochastic Games, (joint with David Leslie and Steven Perkins), Journal of Economic Theory, 189 (2020), 105095
Convergence of best response dynamics in extensive-form games, Journal of Economic Theory, 162 (2016), 21–54, Supplementary Materials.
Abstract: We compare the notion of a tenable block with evolutionary stability and strategic stability, respectively. We show that in addition to the many desired properties of these two stability notions, a tenable block has the property of relative robustness and can reveal concentrated interaction in some large-scale games. Finally, we propose a solution concept using the joint force of strategic stability and coarse tenability.
An Epsilon-committed Cheap-talk Game
Abstract: We apply a consideration-set game (Myerson and Weibull, 2015) to model a partial commitment in the form of strategy constraints. We study the continuous-time best-response dynamic in a consideration-set game with epsilon strategy constraints. In the case where the underlying game is a two-player common-payoff game with cheap talk, we show that if for one player role there is a certain epsilon constraint biased towards the efficient outcome, then the best-response dynamic from a generic initial state must approach the efficient outcome, regardless of the epsilon constraint for the other player role.
Convergence of Best-response Dynamics in Potential Games
Abstract: We prove that the continuous-time joint strategy best-response dynamic from a generic initial point converges to a pure-strategy Nash equilibrium in an ordinal potential game under a minor condition for the payoff matrix.
Evolution in Coordination Games with Cheap Talk
Abstract: This paper presents a collection of results on evolutionary stability and convergence of the continuous-time best-response dynamic in a cheap-talk game with a coordination base game. We first show that from a generic initial point in a cheap-talk game, the best-response dynamic converges to a neutrally stable strategy (NSS) outcome. We then characterize the set of NSS in a cheap-talk game. Finally, for a variation of a cheap-talk population game where an arbitrarily small proportion of the population is committed to playing certain strategies, we show that the best-response dynamic from a generic initial point converges to either an evolutionarily stable strategy (ESS) or a globally efficient outcome.
Stochastic stability in finite extensive-form games of perfect information, SSE/EFI Working Paper Series in Economics and Finance No. 743, March 2013
Abstract: We consider a basic stochastic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. Following Young's papers, we call a state stochastically stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. We prove that, for all finite extensive-form games of perfect information, the best-reply dynamic converges to a Nash equilibrium almost surely. Moreover, only Nash equilibria can be stochastically stable. We present a `centipede-trust game', where we prove that both the backward induction equilibrium component and the Pareto-dominant equilibrium component are stochastically stable, even when the populations increase to infinity. For finite extensive-form games of perfect information, we give a sufficient condition for stochastic stability of the set of non-backward-induction equilibria, and show how much extra payoff is needed to turn an equilibrium stochastically stable.
The instability of backward induction in evolutionary dynamics, (2012) Revised version of Discussion Paper Series 633, the Center for the Study of Rationality, Hebrew University of Jerusalem
Abstract: This paper continues the work initiated in the paper above. We adopt the same model as in the paper above. We show that the non-backward-induction equilibrium component may be stochastically stable for any population size in a finite stopping game where the two equilibrium components are terminated by different players. An unexpected result is that the backward induction equilibrium component may not be stochastically stable for large populations. Finally, we study the stochastic stability result in a different limiting process where the expected number of mutations per generation is bounded away from both zero and infinity.
Fast evolution and a robustness index of backward induction, (2012) Revised version of Discussion Paper Series 632, the Center for the Study of Rationality, Hebrew University of Jerusalem
Abstract: We consider a fast evolutionary dynamic process on finite stopping games, where each player at each node has at most one move to continue the game. A state is stochastically stable if its long-run relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. The fast dynamic process allows each individual in each population to change its strategy at every stage. We define a robustness index of backward induction and show examples where the backward induction equilibrium component is not stochastically stable for large populations. We show some sufficient conditions for stochastic stability, which are different from the ones for the conventional evolutionary model. Even for this fast dynamic process, the transition between any two Nash equilibrium components may take very long time. We also present a two-player best-reply learning process on an extensive-form game which is equivalent to the fast evolutionary process on the associated population game.
A stochastic Ramsey theorem, Journal of Combinatorial Theory, Series A, 118 (2011), 1392–1409.