On the preservation of cooperation in two-strategy games with nonlocal interactions

Ozgur Aydogmus, Wen Zhou, Yun Kang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models.

Original languageEnglish (US)
Pages (from-to)25-42
Number of pages18
JournalMathematical Biosciences
Volume285
DOIs
StatePublished - Mar 1 2017

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Nonlocal Interactions
Preservation
Game
Population
Ecosystem
Evolutionary Strategy
Evolutionary Dynamics
Theoretical Models
Viruses
Pressure
Mutation
Integrodifferential equations
Interaction
Partial differential equations
preserves
Prisoner's Dilemma Game
Evolutionary Game
Wave Speed
Invasion
mutation

Keywords

  • Evolutionary game
  • Integro-differential replicator equations
  • Nonlocal interaction
  • Selections in genetic games

ASJC Scopus subject areas

  • 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

On the preservation of cooperation in two-strategy games with nonlocal interactions. / Aydogmus, Ozgur; Zhou, Wen; Kang, Yun.

In: Mathematical Biosciences, Vol. 285, 01.03.2017, p. 25-42.

Research output: Contribution to journalArticle

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