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Optimal Migration Promotes The Outbreak Of Cooperation In Heterogeneous Populations

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  • FRANK SCHWEITZER

    (ETH Zurich, Kreuzplatz 5, 8032 Zurich, Switzerland)

  • LAXMIDAR BEHERA

    (Department of Electrical Engineering, Indian Institute of Technology, Kanpur, 208 016, India)

Abstract

We consider a population of agents that are heterogeneous with respect to (i) their strategy when interactingngtimes with other agents in an iterated prisoners dilemma game, (ii) their spatial location onKdifferent islands. After each generation, agents adopt strategies proportional to their average payoff received. Assuming a mix of two cooperating and two defecting strategies, we first investigate for isolated islands the conditions for an exclusive domination of each of these strategies and their possible coexistence. This allows to define a threshold frequency for cooperation that, dependent onngand the initial mix of strategies, describes the outbreak of cooperation in the absence of migration. We then allow migration of a fixed fraction of the population after each generation. Assuming a worst case scenario where all islands are occupied by defecting strategies, whereas only one island is occupied by cooperators at the threshold frequency, we determine the optimal migration rate that allows the outbreak of cooperation onallislands. We further find that the threshold frequency divided by the number of islands, i.e., the relative effort for invading defecting islands with cooperators decreases with the number of islands. We also show that there is only a small bandwidth of migration rates, to allow the outbreak of cooperation. Larger migration rates destroy cooperation.

Suggested Citation

  • Frank Schweitzer & Laxmidar Behera, 2012. "Optimal Migration Promotes The Outbreak Of Cooperation In Heterogeneous Populations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-27.
    • Handle: RePEc:wsi:acsxxx:v:15:y:2012:i:supp0:n:s0219525912500592
    DOI: 10.1142/S0219525912500592
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    References listed on IDEAS

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    1. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521775908, January.
    2. Michael D. Cohen & Rick L. Riolo & Robert Axelrod, 1999. "The Emergence of Social Organization in the Prisoner's Dilemma: How Context-Preservation and Other Factors Promote Cooperation," Working Papers 99-01-002, Santa Fe Institute.
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    Cited by:

    1. Frank Schweitzer & Luca Verginer & Giacomo Vaccario, 2020. "Should The Government Reward Cooperation? Insights From An Agent-Based Model Of Wealth Redistribution," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-19, November.
    2. Zhong, Li-Xin & Xu, Wen-Juan & He, Yun-Xin & Zhong, Chen-Yang & Chen, Rong-Da & Qiu, Tian & Shi, Yong-Dong & Ren, Fei, 2017. "A generalized public goods game with coupling of individual ability and project benefit," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 73-80.
    3. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & Zhong, Chen-Yang & Qiu, Tian & Shi, Yong-Dong & Wang, Li-Liang, 2016. "A generalized voter model with time-decaying memory on a multilayer network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 95-105.
    4. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & Qiu, Tian & Shi, Yong-Dong & Zhong, Chen-Yang, 2015. "Coupled effects of local movement and global interaction on contagion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 482-491.
    5. Li-Xin Zhong & Wen-Juan Xu & Yun-Xin He & Chen-Yang Zhong & Rong-Da Chen & Tian Qiu & Yong-Dong Shi & Fei Ren, 2017. "A generalized public goods game with coupling of individual ability and project benefit," Papers 1702.07423, arXiv.org, revised May 2017.

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