![]() ![]() With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player-two-strategy games. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation but without migration, cooperation can not be established throughout the network of demes. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. Our results may provide insights into understanding coevolutionary dynamics of expulsive and cooperative behavior in social dilemma situations. Interestingly, there exists an optimal value of time scale parameter that results in the maximum fraction of altruistic players, which resembles the coherence resonance phenomenon in dynamical systems. For intermediate ranges, we investigate numerically the coupled interplay between pairwise interaction dynamics and strategy updating dynamics, and show that the validity of main results for the limiting case can be extended to this general case. Phase diagrams reveal the occurrence of frozen as well as dynamical stationary states, between which continuous or discontinuous phase transition may happen. Using the extended pair approximation methods and Monte Carlo simulations, we show that the introduction of expellers not only promotes coevolution of expulsion and cooperation by means of both direct and indirect domain competition but also opens the gate to rich dynamical behaviors even if expulsion is costly. ![]() In more realistic spatial settings, we provide both analytical and numerical results for the limiting case where pairwise interaction dynamics proceeds much faster than strategy updating dynamics. ![]() In the mean-field limit, our theoretical analysis of prisoner's dilemma with expellers shows that the increment of either vacant sites ratio or time scale parameter between pairwise interaction process and strategy updating process can slow down evolutionary speed though defection is the only stable fixed point anyway. expellers) are able to banish defectors from their own neighborhoods. In the context of prisoner's dilemma, we present a simple game-theoretical model of expulsion in which punishing cooperators (i.e. Expulsion refers to the widespread behavior of expelling intruders from the owners' territories, which has not been considered in current models on the evolutionary dynamics of cooperation so far. ![]()
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