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Cooperation in Social Dilemmas

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Social Self-Organization

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics, and quantifies the outcomes by payoffs. The prisoner’s dilemma (PD) describes situations in which it is profitable if everybody cooperates rather than defects (free-rides or cheats), but as cooperation is risky and defection is tempting, the expected outcome is defection. Nevertheless, some biological and social mechanisms can support cooperation by effectively transforming the payoffs. Here, we study the related phase transitions, which can be of first order (discontinous) or of second order (continuous), implying a variety of different routes to cooperation. After classifying the transitions into cases of equilibrium displacement, equilibrium selection, and equilibrium creation, we show that a transition to cooperation may take place even if the stationary states and the eigenvalues of the replicator equation for the PD stay unchanged. Our example is based on adaptive group pressure, which makes the payoffs dependent on the endogeneous dynamics in the population. The resulting bistability can invert the expected outcome in favor of cooperation.

This chapter reprints a previous publication with kind permission of the Americal Physical Society. It is requested to cite this work as follows: D. Helbing and S. Lozano (2010) Phase transitions to cooperation in the prisoner’s dilemma. Physical Review E 81(5), 057102. DOI: 10.1103/PhysRevE.81.057102.

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Acknowledgements

This work was partially supported by the Future and Emerging Technologies programme FP7-COSI-ICT of the European Commission through the project QLectives (grant no.: 231200).

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Authors and Affiliations

  1. CLU E1, ETH Zurich, Clausiusstrasse 50, 8092, Zurich, Switzerland

    Dirk Helbing (Chair of Sociology, in particular of Modeling and Simulation)

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  1. Dirk Helbing
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Editors and Affiliations

  1. Lehrstuhl Soziologie, CLU E1, ETH Zürich, Clausiusstr. 50, Zürich, 8092, Switzerland

    Dirk Helbing

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Helbing, D. (2012). Cooperation in Social Dilemmas. In: Helbing, D. (eds) Social Self-Organization. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24004-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-24004-1_6

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  • Print ISBN: 978-3-642-24003-4

  • Online ISBN: 978-3-642-24004-1

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