Strategic Information Exchange

TL;DR

This paper investigates how two players in repeated games with private information can exchange information over time, showing that with sufficiently valuable private info, equilibrium payoffs approach the feasible and rational set as players become more patient.

Contribution

It demonstrates that private information exchange can be sustained in equilibrium, and characterizes the equilibrium payoff set as players become increasingly patient.

Findings

Equilibrium payoffs converge to feasible and individually rational payoffs.

Private information is exchangeable when it is valuable to the other player.

The convergence occurs as players' patience increases.

Abstract

We study a class of two-player repeated games with incomplete information and informational externalities. In these games, two states are chosen at the outset, and players get private information on the pair, before engaging in repeated play. The payoff of each player only depends on his `own' state and on his own action. We study to what extent, and how, information can be exchanged in equilibrium. We prove that provided the private information of each player is valuable for the other player, the set of sequential equilibrium payoffs converges to the set of feasible and individually rational payoffs as players become patient.