Robust equilibria under non-common priors

Abstract : This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.
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Submitted on : Tuesday, November 20, 2012 - 9:42:11 AM
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Daisuke Oyama, Olivier Tercieux. Robust equilibria under non-common priors. Journal of Economic Theory, Elsevier, 2010, 145 (2), pp.752-784. ⟨10.1016/j.jet.2009.10.009⟩. ⟨halshs-00754466⟩

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