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Thermodynamics of evolutionary games
Michigan State University, East Lansing, United States.ORCID iD: 0000-0002-4872-1961
2018 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 6, article id 062136Article in journal (Refereed) Published
Abstract [en]

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the public goods game with three players and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems. © 2018 American Physical Society.

Place, publisher, year, edition, pages
American Physical Society , 2018. Vol. 97, no 6, article id 062136
Keywords [en]
Biology, Defects, Dynamics, Phase transitions, Spin dynamics, Thermodynamics, Evolution of cooperation, Evolutionary games, Expectation values, Hamiltonian dynamics, Long range interactions, Low-dimensional spin systems, Public goods games, Unsolved problems, Hamiltonians, article, expectation, human, magnetic field, mining, phase transition, punishment
National Category
Evolutionary Biology
Identifiers
URN: urn:nbn:se:du-37168DOI: 10.1103/PhysRevE.97.062136Scopus ID: 2-s2.0-85049051368OAI: oai:DiVA.org:du-37168DiVA, id: diva2:1557902
Available from: 2021-05-27 Created: 2021-05-27 Last updated: 2021-05-27Bibliographically approved

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Hintze, Arend

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CiteExportLink to record
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  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • chicago-author-date
  • chicago-note-bibliography
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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