Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2020, Volume 88, Issue 2

Generalized Belief Operator and Robustness in Binary-Action Supermodular Games
p. 693-726

Daisuke Oyama, Satoru Takahashi

This paper studies the robustness of an equilibrium to incomplete information in binary‐action supermodular games. Using a generalized version of belief operator, we explore the restrictions that prior beliefs impose on higher order beliefs. In particular, we obtain a nontrivial lower bound on the probability of a common belief event, uniform over type spaces, when the underlying game has a monotone potential. Conversely, when the game has no monotone potential, we construct a type space with an arbitrarily high probability event in which players never have common belief about that event. As an implication of these results, we show for generic binary‐action supermodular games that an action profile is robust to incomplete information if and only if it is a monotone potential maximizer. Our study offers new methodology and insight to the analysis of global game equilibrium selection.

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Supplement to "Generalized Belief Operator and Robustness in Binary-Action Supermodular Games"

This appendix contains material not found within the manuscript.