Evolution of cooperation under a generalized death-birth process

Abstract

According to the evolutionary death-birth protocol, a player is chosen randomly to die and neighbors compete for the available position proportional to their fitness. Hence, the status of the focal player is completely ignored and has no impact on the strategy update. In this work, we revisit and generalize this rule by introducing a weight factor to compare the payoff values of the focal and invading neighbors. By means of evolutionary graph theory, we analyze the model on joint transitive graphs to explore the possible consequences of the presence of a weight factor. We find that focal weight always hinders cooperation under weak selection strength. Surprisingly, the results show a non-trivial tipping point of the weight factor where the threshold of cooperation success shifts from positive to negative infinity. Once focal weight exceeds this tipping point, cooperation becomes unreachable. Our theoretical predictions are confirmed by Monte Carlo simulations on a square lattice of different sizes. We also verify the robustness of the conclusions to arbitrary two-player prisoner's dilemmas, to dispersal graphs with arbitrary edge weights, and to interaction and dispersal graphs overlapping arbitrarily.

arXiv comment8 two-column pages, 2 figures, accepted for publication in Physical Review E

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• Evolutionary dynamics in stochastic nonlinear public goods games
• The conflict between self-interaction and updating passivity in the evolution of cooperation
• Reputation-based synergy and discounting mechanism promotes cooperation
• When greediness and self-confidence meet in a social dilemma
• Evolution of trust in structured populations
• Evolutionary dynamics of collective decision-making with local social influence on static and dynamic networks