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Triggers for cooperative behavior in the thermodynamic limit: a case study in Public goods game

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  • Colin Benjamin
  • Shubhayan Sarkar

Abstract

In this work, we aim to answer the question: what triggers cooperative behavior in the thermodynamic limit by taking recourse to the Public goods game. Using the idea of mapping the 1D Ising model Hamiltonian with nearest neighbor coupling to payoffs in the game theory we calculate the Magnetisation of the game in the thermodynamic limit. We see a phase transition in the thermodynamic limit of the two player Public goods game. We observe that punishment acts as an external field for the two player Public goods game triggering cooperation or provide strategy, while cost can be a trigger for suppressing cooperation or free riding. Finally, reward also acts as a trigger for providing while the role of inverse temperature (fluctuations in choices) is to introduce randomness in strategic choices.

Suggested Citation

  • Colin Benjamin & Shubhayan Sarkar, 2018. "Triggers for cooperative behavior in the thermodynamic limit: a case study in Public goods game," Papers 1804.06465, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1804.06465
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    Cited by:

    1. Correia, A.D. & Leestmaker, L.L. & Stoof, H.T.C. & Broere, J.J., 2022. "Asymmetric games on networks: Towards an Ising-model representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    2. Colin Benjamin & Arjun Krishnan U.M., 2023. "Nash equilibrium mapping vs. Hamiltonian dynamics vs. Darwinian evolution for some social dilemma games in the thermodynamic limit," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(7), pages 1-16, July.

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