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Cooperation risk and Nash equilibrium: Quantitative description for realistic players

Author

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  • Nakamura, G.M.
  • Contesini, G.S.
  • Martinez, A.S.

Abstract

The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential games approach by taking into account the inherent risks of cooperation. We show the Public Goods game reduce to a Hamiltonian with one-body operators, with the correct Nash Equilibrium as the ground state. The inclusion of punishments to the Public Goods game reduces cooperation risks, creating two-body interactions with a rich phase diagram, in which phase transitions segregates cooperative from competitive regimes.

Suggested Citation

  • Nakamura, G.M. & Contesini, G.S. & Martinez, A.S., 2019. "Cooperation risk and Nash equilibrium: Quantitative description for realistic players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 102-111.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:102-111
    DOI: 10.1016/j.physa.2018.09.194
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    References listed on IDEAS

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    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Rand, David Gertler & Dreber, Anna & Fudenberg, Drew & Ellingson, Tore & Nowak, Martin A., 2009. "Positive Interactions Promote Public Cooperation," Scholarly Articles 3804483, Harvard University Department of Economics.
    3. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
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    Cited by:

    1. Changping Zhao & Xiya Xie & Jun Song, 2021. "Complex Network Game Model Simulation of Arctic Sustainable Fishery Trade Cooperation under COVID-19," Sustainability, MDPI, vol. 13(14), pages 1-17, July.

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