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Title: Evolutionary dynamics of the prisoner's dilemma with expellers
Authors: Wang, XF
Zhang, GF 
Kong, WJ
Keywords: Expulsion
Phase separation
Evolutionary dynamics
Social dilemma
Issue Date: 2019
Publisher: Institute of Physics Publishing
Source: Journal of physics communications, Jan. 2019, v. 3, no. 1, 015011, p. 1-25 How to cite?
Journal: Journal of physics communications 
Abstract: 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. In the context of prisoner's dilemma, we present a simple game-theoretical model of expulsion in which punishing cooperators (i.e. expellers) are able to banish defectors from their own neighborhoods. 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. 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. 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. Phase diagrams reveal the occurrence of frozen as well as dynamical stationary states, between which continuous or discontinuous phase transition may happen. 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. 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. Our results may provide insights into understanding coevolutionary dynamics of expulsive and cooperative behavior in social dilemma situations.
EISSN: 2399-6528
DOI: 10.1088/2399-6528/aafe57
Rights: Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence ( Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
© 2019 The Author(s). Published by IOP Publishing Ltd
The following publication Wang, X. F., Zhang, G. F., & Kong, W. J. (2019). Evolutionary dynamics of the prisoner's dilemma with expellers. Journal of Physics Communications, 3(1), 015011, 1-25 is available at
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