2 research outputs found
Punishment in Public Goods games leads to meta-stable phase transitions and hysteresis
The evolution of cooperation has been a perennial problem in evolutionary
biology because cooperation can be undermined by selfish cheaters who gain an
advantage in the short run, while compromising the long-term viability of the
population. Evolutionary game theory has shown that under certain conditions,
cooperation nonetheless evolves stably, for example if players have the
opportunity to punish cheaters that benefit from a public good yet refuse to
pay into the common pool. However, punishment has remained enigmatic because it
is costly, and difficult to maintain. On the other hand, cooperation emerges
naturally in the Public Goods game if the synergy of the public good (the
factor multiplying the public good investment) is sufficiently high. In terms
of this synergy parameter, the transition from defection to cooperation can be
viewed as a phase transition with the synergy as the critical parameter. We
show here that punishment reduces the critical value at which cooperation
occurs, but also creates the possibility of meta-stable phase transitions,
where populations can "tunnel" into the cooperating phase below the critical
value. At the same time, cooperating populations are unstable even above the
critical value, because a group of defectors that are large enough can
"nucleate" such a transition. We study the mean-field theoretical predictions
via agent-based simulations of finite populations using an evolutionary
approach where the decisions to cooperate or to punish are encoded genetically
in terms of evolvable probabilities. We recover the theoretical predictions and
demonstrate that the population shows hysteresis, as expected in systems that
exhibit super-heating and super-cooling. We conclude that punishment can
stabilize populations of cooperators below the critical point, but it is a
two-edged sword: it can also stabilize defectors above the critical point.Comment: 22 pages, 9 figures. Slight title change, version that appears in
Physical Biolog