Games with Incomplete Information When Players are Partially Aware of Others' Signals

Abstract

Empirical and experimental findings suggest that players may underestimate others' private information in incomplete-information games. We modify standard epistemic assumptions of static incomplete-information games to allow partial signal-awareness. That is, players can be unaware of some of the signals available to others. When learning to play, players form conjectures that underrepresent the sophistication of others' strategy profile. The resulting solution concept is equilibrium with partial signal-awareness (EPSA). We illustrate EPSA by various examples and prove an existence result and an equivalence result between it and Bayesian Nash equilibrium. We then compare EPSA and analogy-based expectation equilibrium (ABEE) (Jehiel and Koessler, 2008) and prove an equivalence result between them for analogy-based expectation games that satisfy the condition of comparative-informativeness. We also discuss how they differ.

Keywords: games with incomplete information, partial signal-awareness, analogy-based expectation equilibrium, cursed equilibrium, coarse reasoning, bounded rationality

JEL Classification: C7, D8