Observations on Cooperation

TL;DR

This paper investigates how cooperation can be maintained among agents in a Prisoner's Dilemma setting with limited observations, the presence of committed types, and various information structures, proposing a robust strategy for sustaining cooperation.

Contribution

It introduces a novel strategy combination that sustains cooperation even with committed agents and characterizes its uniqueness and robustness under stationarity assumptions.

Findings

The proposed strategy sustains cooperation in diverse environments.

Committed agents destabilize previous cooperation mechanisms.

The strategy is essentially unique under stationarity and robust to perturbations.

Abstract

We study environments in which agents are randomly matched to play a Prisoner's Dilemma, and each player observes a few of the partner's past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.