Evolution of cooperation with time-varying tags and heterogeneous immigration dynamics

Cooperation in an open dynamic system fundamentally depends upon information distributed across its components. Yet in an environment with rapidly evolving complexity, this information may need to change adaptively to enable cooperative interactions. Combining the methods of evolutionary game theory, agent-based simulation, and statistical physics, we develop a model of the evolution of cooperation in an ageing population of artificial decision makers playing spatial tag-mediated prisoner’s dilemma games with their ingroup neighbors and with genetically unrelated immigrant agents. We introduce the concept of time-varying tags such that the phenotypic features of ‘new’ agents can change into ‘approved’ following variable approval times. In the standard 4-strategy model with fixed tags, we identified a critical cost ccrit above which cooperation transitioned abruptly into the phase of pure defection. In our generalized 6-strategy model with time-varying tags, the maintenance of elevated cooperation was observed for a much wider region of the parameter space, peaking at intermediate approval times and cost values above ccrit. Our findings reveal the existence of optimal approval times leading to high levels of cooperation if a fraction of the population adopts the strategy with an egalitarian generosity directed towards both native and approved agents, regardless of their actual origin.