Ex-Post Equilibria: Structure and Computation

2026-08-07

AI Summary

This study addresses the existence, structure, and computation of ex post equilibria (EPE) in simultaneous-move games under parameter uncertainty. By introducing two key properties—monotonicity and set consistency—it provides the first complete structural characterization of EPE and, in cases where no exact equilibrium exists, proposes the notion of an “optimal approximate ex post equilibrium.” Focusing on two important classes of games—zero-sum and concave potential games—the work develops an efficient computational framework leveraging a minimax auxiliary formulation. Theoretical analysis elucidates the structural properties and computational complexity of EPE, offering new equilibrium concepts and algorithmic foundations for games with incomplete information.

Abstract

This paper studies ex-post equilibria (EPEs) in simultaneous-move games with parameter uncertainty. We first compare EPEs with existing notions of robust equilibrium and provide a general foundation for EPEs as a solution concept for games with parameter uncertainty, and we show that EPEs are fully characterized by two game-theoretic properties (monotonicity and set-consistency). Since ex-post equilibria may fail to exist, we introduce the notion of an optimal approximate ex-post equilibrium, in which players adopt approximate best responses while minimizing the degree of suboptimality. We study the problem of computing EPEs and optimal approximate EPEs, focusing on two important classes of games: zero-sum games and concave potential games. We provide several hardness results, as well as a general class of computational approaches based on auxiliary minimax formulations.

Problem

• ex-post equilibrium
• parameter uncertainty
• simultaneous-move games
• approximate equilibrium
• equilibrium computation

Innovation

• ex-post equilibrium
• parameter uncertainty
• approximate equilibrium
• minimax formulation
• computational hardness