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Two-strategy games with time constraints on regular graphs.

Mark Broom1, Vlastimil Křivan2

  • 1Department of Mathematics, City, University of London, London, UK.

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Summary
This summary is machine-generated.

This study integrates spatial structure and time constraints in evolutionary game theory. Lower neighbour counts can promote cooperation in Prisoner's Dilemma games, depending on population dynamics.

Keywords:
Birth-death and death-birth updatingEvolutionary game theoryGames on regular graphsHawk-Dove gamePrisoner’s dilemma

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Area of Science:

  • Evolutionary game theory
  • Mathematical biology
  • Theoretical ecology

Background:

  • Traditional evolutionary game models simplify populations, ignoring spatial structure and time constraints.
  • Evolutionary graph theory addresses spatial effects in non-homogeneous populations.
  • Time constraint theory accounts for variable event durations and strategy-dependent interactions.

Purpose of the Study:

  • To develop a novel model combining spatial structure (graphs) and time constraints in evolutionary games.
  • To investigate the impact of graph degree and population dynamics (birth-death, death-birth) on game outcomes.
  • To analyze strategy evolution in Hawk-Dove and Prisoner's Dilemma games under these combined conditions.

Main Methods:

  • Modelling populations on graphs with two distinct time scales: short-term interactions and long-term evolution.
  • Implementing birth-death and death-birth population dynamics on the graph structure.
  • Analyzing the emergence of Evolutionarily Stable Strategies (ESS) in relation to graph degree and dynamics.

Main Results:

  • For high-degree graphs, results align with well-mixed models, showing two ESSs in Hawk-Dove and Prisoner's Dilemma.
  • Low-degree graphs reveal significant differences, particularly with death-birth dynamics.
  • Decreasing graph degree generally promotes mixed ESSs, facilitating cooperation in Prisoner's Dilemma.

Conclusions:

  • Game solutions are non-trivially dependent on the interplay of graph degree, population dynamics, and game type.
  • Spatial structure and time constraints significantly alter evolutionary game dynamics compared to simpler models.
  • Cooperation is more readily established in spatially structured populations with fewer interactions, especially under specific dynamics.