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Evolutionarily stable payoff matrix in hawk-dove games.

Balázs Király1, Tamás Varga2, György Szabó3,4

  • 1Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary. kiraly.balazs@ek.hun-ren.hu.

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Summary
This summary is machine-generated.

This study introduces an evolutionary model where both strategies and payoff matrices evolve. The research reveals that the cost of escalating fights remains constant during evolution, mirroring natural selection

Keywords:
Asymmetric interactionHawk–dove gameMatrix gameTrait evolution

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Area of Science:

  • Evolutionary Game Theory
  • Behavioral Ecology
  • Theoretical Biology

Background:

  • Classical matrix game models assume fixed interaction outcomes for behavioral evolution.
  • This study introduces a novel evolutionary model where strategies and payoff matrices co-evolve under natural selection.

Purpose of the Study:

  • To develop an evolutionary model incorporating evolving payoff matrices.
  • To investigate the dynamics of fighting ability and its impact on evolutionary stability.
  • To define and analyze evolutionarily stable phenotypes in this dynamic framework.

Main Methods:

  • Extended the hawk-dove matrix game with an evolving phenotypic trait for fighting ability.
  • Modeled the probability of winning and cost of losing in escalated hawk-hawk fights.
  • Defined evolutionarily stable phenotypes including strategy, trait, and payoff matrix.

Main Results:

  • Identified evolutionarily stable phenotypes comprising stable strategies, traits, and payoff matrices.
  • Demonstrated that the maximal cost of escalating fights remains constant during evolution.
  • Showcased that the evolutionarily stable phenotype maximizes payoff in hawk-hawk fights.

Conclusions:

  • The cost of escalating fights is stable over evolutionary time, given separated timescales for behavioral and trait selection.
  • Evolutionarily stable phenotypes are products of natural selection, influencing both success criteria and successful forms.
  • Results highlight the dual nature of Darwinian evolution, where selection shapes both traits and the rules of interaction.