Cooperation can emerge in prisoner's dilemma from a multi-species predator prey replicator dynamic

Elisabeth Paulson, Christopher Griffin

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner's dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.

Original languageEnglish (US)
Pages (from-to)56-62
Number of pages7
JournalMathematical Biosciences
Volume278
DOIs
StatePublished - Aug 1 2016

Fingerprint

Replicator Dynamics
Prisoners' Dilemma
Predator-prey
Population Dynamics
Population Density
predators
game animals
Game
Population
Population dynamics
Mixed Strategy
Zero-sum
Finite Models
Finite Population
Population Model
Population Size
population size
population dynamics
Prisoner Dilemma
Proportion

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Medicine(all)
  • Modeling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

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abstract = "In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner's dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.",
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Cooperation can emerge in prisoner's dilemma from a multi-species predator prey replicator dynamic. / Paulson, Elisabeth; Griffin, Christopher.

In: Mathematical Biosciences, Vol. 278, 01.08.2016, p. 56-62.

Research output: Contribution to journalArticle

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