Global sequential equilibrium

Abstract

Abstract This paper extends the solution concept of sequential equilibrium (SE) to games with infinite decision points and actions, thereby introducing global sequential equilibrium (GSE). While qualitatively similar to SE, GSE distinctively defines posteriors globally as whole probability distributions across all information sets in each period, rather than separately at each information set as in SE. The following properties of GSE are demonstrated: Its existence under the conditions of a compact set of strategy profiles (in the weak topology) and bounded and continuous utility functions; its equivalence to SE in finite games; its qualification as a Nash equilibrium and, in games with incomplete information, also as a subgame perfect Nash equilibrium; and its satisfaction of convex structural consistency under the condition of statistical independence of players' types and states. These properties establish GSE as a robust and generalizable extension of SE, with important implications for the analysis of games with infinite types and actions.