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Evan Friedman

Columbia University, New York, USA
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Authors: Evan Friedman and Jeremy Ward

Abstract: We study an equilibrium model in which players make stochastic choices given their beliefs and there is noise in the beliefs themselves. The model primitives are an action- map, which determines a distribution of actions given beliefs, and a belief-map, which determines a distribution of beliefs given opponents’ behavior. These are restricted to satisfy axioms that are stochastic generalizations of “best response” and “correct beliefs”, respectively. In our laboratory experiment, we collect actions data and elicit beliefs for each game within a family of asymmetric 2-player games. These games have systematically varied payoff s, allowing us to “trace out” both the action- and belief-maps. We find that, while both “noise in actions” and “noise in beliefs” are important in explaining observed behaviors, there are systematic violations of the axioms. In particular, although all subjects observe and play the same games, subjects in different roles have qualitatively different belief biases. To explain this, we argue that the player role itself induces a higher degree of strategic sophistication in the player who faces more asymmetric payoffs. This is confirmed by structural estimates.

Keywords: beliefs; quantal response equilibrium; noisy belief equilibrium

JEL Classification: C72, C92, D84
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Full Text: “Stochastic Choice and Noisy Beliefs in Games: an Experiment”