Emergence and resilience of cooperation in the spatial Prisoner's Dilemma via a reward mechanism

TL;DR

This paper demonstrates that a fixed reward mechanism can enable cooperation to emerge and persist in spatial Prisoner's Dilemma settings, even after the reward is removed, through analytical and simulation methods.

Contribution

It introduces a cost-benefit reward formulation that allows a single cooperator to invade and sustain cooperation in a population of defectors, extending prior models.

Findings

A fixed reward enables a single cooperator to invade defectors.

Cooperation structures become resilient even after reward removal.

Large cooperation levels are achievable in the model.

Abstract

We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation.