Nonlinear Dynamics

, Volume 97, Issue 1, pp 749–766 | Cite as

Evolutionary dynamics of cooperation in the public goods game with pool exclusion strategies

  • Linjie Liu
  • Xiaojie ChenEmail author
  • Matjaž Perc
Original Paper


Social exclusion is widely used as a control mechanism to promote cooperative behavior in human societies. However, it remains unclear how such control strategies actually influence the evolutionary dynamics of cooperation. In this paper, we introduce two types of control strategies into a population of agents that play the public goods game, namely prosocial pool exclusion and antisocial pool exclusion, and we use the replicator equation to study the resulting evolutionary dynamics for infinite well-mixed populations. We show that the introduction of prosocial pool exclusion can stabilize the coexistence of cooperators and defectors by means of periodic oscillations, but only in the absence of second-order prosocial pool exclusion. When considering also antisocial pool exclusion, we show that the population exhibits a heteroclinic circle, where cooperators can coexist with other strategists. Moreover, when second-order exclusion is taken into account, we find that prosocial pool exclusion is the dominant strategy, regardless of whether the second-order exclusion is prosocial or antisocial. In comparison with punishment, we conclude that prosocial pool exclusion is a more effective control mechanism to curb free-riding.


Evolutionary dynamics of cooperation Pool exclusion Public goods game Replicator equation 



This research was supported by the National Natural Science Foundation of China (Grant No. 61503062) and by the Slovenian Research Agency (Grant Nos. J1-7009, J4-9302, J1-9112 and P1-0403).

Compliance with ethical standards

Conflict of interest

The authors declare that no competing interest exist.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  3. 3.Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  4. 4.Complexity Science Hub ViennaViennaAustria

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