Exit rights open complex pathways to cooperation

TL;DR

This paper explores how introducing an exit option in the prisoner's dilemma influences cooperation, revealing complex dynamics like coexistence and oscillations depending on population structure and parameters.

Contribution

It demonstrates that adding an exit option creates diverse evolutionary outcomes, including cooperation promotion in well-mixed populations and cyclic dominance in networks.

Findings

Exiters promote cooperation in well-mixed populations with iteration or reputation.

In networked populations, exiters enable coexistence of all three actor types.

Network oscillations can lead to exiters' extinction and defector dominance.

Abstract

We study the evolutionary dynamics of the prisoner's dilemma game in which cooperators and defectors interact with another actor type called exiters. Rather than being exploited by defectors, exiters exit the game in favour of a small payoff. We find that this simple extension of the game allows cooperation to flourish in well-mixed populations when iterations or reputation are added. In networked populations, however, the exit option is less conducive to cooperation. Instead, it enables the coexistence of cooperators, defectors, and exiters through cyclic dominance. Other outcomes are also possible as the exit payoff increases or the network structure changes, including network-wide oscillations in actor abundances that may cause the extinction of exiters and the domination of defectors, although game parameters should favour exiting. The complex dynamics that emerges in the wake of a simple option to exit the game implies that nuances matter even if our analyses are restricted to incentives for rational behaviour.