Information Spillover in Multiple Zero-sum Games

TL;DR

This paper analyzes how information spillover affects the equilibrium payoffs in a three-player Bayesian game with two simultaneous zero-sum interactions, highlighting conditions for overcoming adverse effects and potential severity.

Contribution

It generalizes existing models to a three-player setting and characterizes how information spillover impacts equilibrium payoffs, providing conditions for mitigation.

Findings

Conditions for fully overcoming adverse spillover effects

Characterization of equilibrium payoffs under spillover

Potential severity of spillover effects on payoffs

Abstract

This paper considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of the Aumann et al. [1] two-player zero-sum one-sided incomplete information model. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long-term average payoffs. Our objective is to understand the adverse effects of \information spillover" from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects and characterize equilibrium payoffs. In a second result, we show how the effects of information spillover on the equilibrium payoff set of the informed player might be severe.