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Related Experiment Videos

Long-range prisoner's dilemma game on a cycle.

Jiwon Bahk1, Seung Ki Baek2, Hyeong-Chai Jeong1

  • 1Department of Physics and Astronomy, Sejong University, Seoul 05006, Korea.

Physical Review. E
|February 21, 2019
PubMed
Summary

This study explores how altruism evolves with long-range interactions using a Prisoner's Dilemma game model. Altruism can proliferate when the cost of cooperation is below a calculated threshold, depending on interaction and competition exponents.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Social Dynamics

Background:

  • Understanding the evolution of cooperation and altruism is a fundamental challenge in evolutionary biology.
  • Previous models often focused on short-range interactions, limiting applicability to diverse ecological and social systems.
  • The Prisoner's Dilemma (PD) game provides a framework for studying strategic interactions, but its application to spatial dynamics with varying interaction ranges requires further investigation.

Purpose of the Study:

  • To investigate the evolutionary dynamics of altruism in a spatial model with long-range interactions.
  • To determine the conditions under which altruistic behaviors can proliferate on a cycle under algebraic decay of interaction and competition probabilities.
  • To analytically and numerically derive the threshold cost for the prevalence of altruism.

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Main Methods:

  • A simplified Prisoner's Dilemma (PD) game model was employed, parameterized by the cost of cooperation (c).
  • Interaction and competition probabilities were defined to decay algebraically with distance (r_{AB}) using exponents α and β, respectively.
  • Analytical solutions were derived for the limiting case β→∞ (nearest-neighbor competition), and a numerical method was developed for finite β.

Main Results:

  • An analytical condition (c_{th}) for the proliferation of altruism was derived for nearest-neighbor competition (β→∞).
  • A conjecture for c_{th} as a function of α and β was proposed for finite interaction/competition ranges.
  • Numerical simulations showed excellent agreement with the conjectured formula, even under significant selection pressure.

Conclusions:

  • Long-range interactions, modulated by specific decay exponents (α, β), significantly influence the evolutionary stability of altruism.
  • The study provides a quantitative framework for understanding altruism's spread in spatially structured populations with non-local interactions.
  • The findings offer insights into the conditions favoring cooperation in diverse systems, from microbial communities to social networks.