Sophisticated play by idiosyncratic agents

Agents are drawn from a large population and matched to play a symmetric coordination game, the payoffs of which are perturbed by agent-specific heterogeneity. Individuals observe a (possibly sampled) history of play, which forms the initial hypothesis for an opponent's behaviour. Using this hypothesis as a starting point, the agents iteratively reason toward a Bayesian Nash equilibrium. When sampling is complete and the noise becomes vanishingly small, a single equilibrium is played almost all the time. A necessary and sufficient condition for selection, shown to be closely related (but not identical) to risk-dominance, is derived. When sampling is sufficiently incomplete, the risk-dominant equilibrium is played irrespective of the history observed.JEL Classification: C72, C73The authors thank Tom Norman, Kevin Roberts, Hyun Shin, Peyton Young, the editor and an anonymous referee for helpful comments. Correspondence to: C. Wallace     

-Best response set

This paper introduces a notion of p-best response set (p-BR). We build on this notion in order to provide a new set-valued concept: the minimal p-best response set (p-MBR). After proving general existence results of the p-MBR, we show that it characterizes set-valued stability concepts in a dynamic with Poisson revision opportunities borrowed from Matsui and Matsuyama [An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415–434.] Then, we study equilibrium selection. In particular, using our notion of p-BR, we generalize Morris et al. [p-Dominance and belief potential, Econometrica 63 (1995) 145–157.] that aimed to provide sufficient conditions under which a unique equilibrium is selected in the presence of higher order uncertainty.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.