Cooperation under Incomplete Information on the Discount Factors

TL;DR

This paper analyzes the conditions under which grim-trigger strategies form equilibria in repeated Prisoner's Dilemma games with incomplete information about players' discount factors, extending the understanding of cooperation stability.

Contribution

It provides necessary and sufficient conditions for grim-trigger strategies to be equilibria under incomplete information about discount factors.

Findings

Characterizes when grim-trigger strategies are equilibria with incomplete info.

Identifies conditions for cooperation in incomplete information settings.

Shows how cooperation events relate to complete information scenarios.

Abstract

In the repeated Prisoner's Dilemma, when every player has a different discount factor, the grim-trigger strategy is an equilibrium if and only if the discount factor of each player is higher than some threshold. What happens if the players have incomplete information regarding the discount factors? In this work we look at repeated games in which each player has incomplete information regarding the other player's discount factor, and ask when a pair of grim-trigger strategies is an equilibrium. We provide necessary and sufficient conditions for such strategies to be an equilibrium. We characterize the states of the world in which the strategies are not triggered, i.e., the players cooperate, in such equilibria (or $\epsilon$-equilibria), and ask whether these "cooperation events" are close to those in the complete information case, when the information is "almost" complete, in several senses.