Extensive Form Generalized Games

Abstract

This paper introduces extensive form generalized games, a general framework for modeling dynamic strategic settings where players' feasible strategies depend on the strategies chosen by others. Extensive form generalized games nest a variety of existing game theoretic frameworks, including games with bounded rationality, endogenous information acquisition, rationally inattentive players, and games played by finite automata. Sufficient conditions for the existence of equilibria in behavioral strategies are provided for finite extensive form generalized games, and are shown to be tight. The most salient of these conditions, generalized perfect recall, is a generalized convexity condition which is equivalent to perfect recall in standard extensive form games. Feasibility correspondences describing rational inattention are shown to satisfy generalized perfect recall, and a notion of perfection is introduced to rule out incredible self restraint, a novel type of incredible threat in these settings.