The Maxmin Value of Repeated Games with Incomplete Information on One Side and Tail-Measurable Payoffs

2025/12/01 by Koltun, Gil Bar Castellon, Lehrer, Ehud, Solan, Eilon
#91A05 #91A10 #91A20 #91A27 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2512.01581

Abstract

We study two-player zero-sum repeated games with incomplete information on one side, where the payoff function is tail measurable (and not necessarily the long-run average payoff). We show that the maxmin value equals the concavification of the value function of the non-revealing game. In addition, we provide an example demonstrating that, under tail-measurable payoffs, the value of the game may fail to exist.

Citations

• Bayesian Persuasion
• Stochastic Games with General Payoff Functions
• Equilibrium in Two-Player Stochastic Games with Shift-Invariant Payoffs
• Regularity of the minmax value and equilibria in multiplayer Blackwell games
• Mertens conjectures in absorbing games with incomplete information

Related

• On repeated zero-sum games with incomplete information and asymptotically bounded values
• The value of Markov Chain Games with incomplete information on both sides
• High Probability Guarantees in Repeated Games: Theory and Applications in Information Theory
• Information Spillover in Multiple Zero-sum Games
• Repeated games of incomplete information with large sets of states