Evolutionary prisoner's dilemma games with optional participation

TL;DR

This study explores how optional participation and cyclic dominance among cooperators, defectors, and loners influence evolutionary dynamics in prisoner's dilemma games on different network structures, revealing patterns like oscillations and self-organization.

Contribution

It introduces a model with optional participation and analyzes its effects on strategy dynamics using simulations and pair approximation, highlighting differences between lattice and random regular graphs.

Findings

Loners prevent spread of defectors and deadlocks.

On lattices, cyclic dominance leads to self-organizing patterns.

On random graphs, oscillatory behaviors depend on temptation to defect.

Abstract

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This results in a rock-scissors-paper type cyclic dominance of the three strategies. The players are located either on square lattices or random regular graphs with the same connectivity. Occasionally, every player reassesses its strategy by sampling the payoffs in its neighborhood. The loner strategy efficiently prevents successful spreading of selfish, defective behavior and avoids deadlocks in states of mutual defection. On square lattices, Monte Carlo simulations reveal self-organizing patterns driven by the cyclic dominance, whereas on random regular graphs different types of oscillatory behavior are observed: the temptation to defect determines whether damped, periodic or increasing oscillations occur. These results are compared to predictions by pair approximation. Although pair approximation is incapable of distinguishing the two scenarios because of the equal connectivity, the average frequencies as well as the oscillations on random regular graphs are well reproduced.