Cooperation under Incomplete Information on the Discount Factors

TL;DR

This paper investigates the conditions under which full cooperation can be sustained in repeated games when players have incomplete information about each other's patience levels, providing a characterization of equilibrium cooperation states.

Contribution

It offers necessary and sufficient conditions for equilibrium cooperation with grim trigger strategies under incomplete information on discount factors.

Findings

Full cooperation can be achieved under specific conditions with incomplete information.

The paper characterizes the states where cooperation occurs in equilibrium.

Cooperation events are close to complete information cases when information is nearly complete.

Abstract

In repeated games, cooperation is possible in equilibrium only if players are sufficiently patient, and long-term gains from cooperation outweigh short-term gains from deviation. What happens if the players have incomplete information regarding each other's discount factors? In this paper we look at repeated games in which each player has incomplete information regarding the other player's discount factor, and ask when full cooperation can arise in equilibrium. We provide necessary and sufficient conditions that allow full cooperation in equilibrium that is composed of grim trigger strategies, and characterize the states of the world in which full cooperation occurs. We then ask whether these "cooperation events" are close to those in the complete information case, when the information on the other player's discount factor is "almost" complete.