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Exit rights open complex pathways to cooperation.

Chen Shen1,2, Marko Jusup2, Lei Shi1

  • 1School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, People's Republic of China.

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|January 13, 2021
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Summary
This summary is machine-generated.

Adding an "exiter" role to the Prisoner's Dilemma game can promote cooperation in well-mixed groups. However, in networked populations, this option leads to complex dynamics and coexistence of strategies.

Keywords:
coexistencecooperationcyclic dominanceevolutionary game theoryoscillations

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Area of Science:

  • Evolutionary Game Theory
  • Behavioral Economics
  • Network Science

Background:

  • The Prisoner's Dilemma is a fundamental model in game theory illustrating the conflict between individual self-interest and collective benefit.
  • Traditional models often focus on cooperators and defectors, overlooking strategic withdrawal as a behavioral option.
  • Understanding cooperation dynamics is crucial in various biological and social systems.

Purpose of the Study:

  • To investigate the evolutionary impact of introducing an 'exiter' strategy into the Prisoner's Dilemma game.
  • To analyze how the exit option affects cooperation in both well-mixed and networked populations.
  • To explore the emergent dynamics and conditions for strategy coexistence.

Main Methods:

  • Agent-based modeling of the Prisoner's Dilemma incorporating cooperators, defectors, and exiters.
  • Simulation of interactions in both randomly mixing populations and structured networks.
  • Analysis of strategy abundances, payoff structures, and cyclic dominance under varying parameters.

Main Results:

  • In well-mixed populations with repeated interactions or reputation, the exit option facilitates the flourishing of cooperation.
  • In networked populations, the exit option leads to cyclic dominance, enabling the coexistence of all three strategies (cooperators, defectors, exiters).
  • Changes in exit payoff or network structure can lead to oscillations, extinction of exiters, or defector dominance.

Conclusions:

  • The introduction of a simple exit option significantly alters the evolutionary dynamics of the Prisoner's Dilemma.
  • Network structure plays a critical role in determining the impact of the exit strategy on cooperation.
  • Complex behavioral outcomes arise from seemingly minor changes in game rules, highlighting the importance of nuanced analysis.