The Shared Reward Dilemma

TL;DR

This paper investigates how sharing a fixed reward among cooperators influences behavior in the Prisoner's Dilemma, revealing complex equilibrium patterns and dynamics through comprehensive analysis.

Contribution

It provides a complete classification of equilibria and evolutionary dynamics in the shared reward Prisoner's Dilemma, a novel extension of traditional cooperation models.

Findings

Multiple equilibrium regimes identified

Complex dynamics depend on reward sharing parameters

Unexpected cooperative behaviors can emerge

Abstract

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically, for a group of players that collect payoffs by playing a pairwise Prisoner's Dilemma game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the $n$-player game as well as of its evolutionary dynamics.