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

TL;DR

This paper investigates the maxmin value in two-player zero-sum repeated games with incomplete information and tail-measurable payoffs, revealing conditions for its existence and characterizing it via concavification.

Contribution

It establishes that the maxmin value equals the concavification of the non-revealing game value function and provides an example where the game value fails to exist.

Findings

Maxmin value equals the concavification of the non-revealing game value.

The game value may fail to exist under tail-measurable payoffs.

Conditions for the existence of the game value are identified.

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.