GENERALIZED BELIEF OPERATOR AND ROBUSTNESS IN BINARY-ACTION SUPERMODULAR GAMES

• 成果类型: Article
• 署名作者: Oyama, Daisuke; Takahashi, Satoru
• 署名单位: University of Tokyo; National University of Singapore
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA17237
• 发表日期: 2020
• 页码: 693-726
• 关键词: Equilibrium selection; global games; COORDINATION; INFORMATION; sets

摘要

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.