Deterministic and stochastic cooperation transitions in evolutionary games on networks
arXiv:2210.01710 · doi:10.1103/PhysRevE.107.054302
Abstract
Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we investigate the critical behavior of evolutionary social dilemmas on structured populations by using the framework of master equations and Monte Carlo simulations. The developed theory describes the existence of absorbing, quasi-absorbing, and mixed strategy states and the transition nature, continuous or discontinuous, between the states as the parameters of the system change. In particular, when the decision-making process is deterministic, in the limit of zero effective temperature of the Fermi function, we find that the copying probabilities are discontinuous functions of the system's parameters and of the network degrees sequence. This may induce abrupt changes in the final state for any system size, in excellent agreement with the Monte Carlo simulation results. Our analysis also reveals the existence of continuous and discontinuous phase transitions for large systems as the temperature increases, which is explained in the mean-field approximation. Interestingly, for some game parameters, we find optimal "social temperatures" maximizing/minimizing the cooperation frequency/density.
14 pages, 5 figures
References in corpus (17)
- Statistical physics of social dynamics
- The structure and dynamics of multilayer networks
- Evolutionary games on graphs
- Statistical physics of human cooperation
- Evolutionary dynamics of group interactions on structured populations: A review
- Dynamical Organization of Cooperation in Complex Topologies
- Fixation of strategies for an evolutionary game in finite populations
- Degree mixing in multilayer networks impedes the evolution of cooperation
- Analytical Solution of the Voter Model on Disordered Networks
- Griffiths phases on complex networks
- Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas
- Social Network Reciprocity as a Phase Transition in Evolutionary Cooperation
- Evolution of cooperation driven by zealots
- Strategical incoherence regulates cooperation in social dilemmas on multiplex networks
- Cooperation in regular lattices
- Coordination and equilibrium selection in games: the role of local effects
- Predicting transitions in cooperation levels from network connectivity