Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games
研究了二元行动超模博弈中均衡对不完全信息的稳健性，通过广义信念算子探讨先验信念对高阶信念的限制，并证明行动稳健当且仅当它是单调势最大化者。
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.