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Related Experiment Videos

Evolutionary cycles of cooperation and defection.

Lorens A Imhof1, Drew Fudenberg, Martin A Nowak

  • 1Institut für Gesellschafts und Wirtschaftswissenschaften, Statistische Abteilung, Universität Bonn, D-53113 Bonn, Germany. limhof@uni-bonn.de

Proceedings of the National Academy of Sciences of the United States of America
|July 27, 2005
PubMed
Summary

In finite populations, evolutionary game theory shows that natural selection can favor cooperation. Oscillations between always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT) strategies can lead to sustained cooperation.

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Area of Science:

  • Evolutionary Game Theory
  • Population Dynamics
  • Behavioral Ecology

Background:

  • Natural selection typically favors defection over cooperation in social dilemmas.
  • The repeated prisoner's dilemma models strategic interactions over multiple encounters.
  • Understanding the evolution of cooperation is crucial for explaining social behavior.

Purpose of the Study:

  • To investigate the evolutionary dynamics of cooperation in finite populations.
  • To analyze the role of mutation-selection in strategy evolution.
  • To compare stochastic dynamics with deterministic predictions.

Main Methods:

  • Simulating mutation-selection dynamics for three strategies: always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT).
  • Analyzing evolutionary oscillations in finite populations.

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  • Examining the long-term time average of strategy frequencies.

    • Main Results:

    • Evolutionary oscillations were observed among ALLD, ALLC, and TFT strategies.
    • The population cycles through these strategies, returning to the starting point.
    • Surprisingly, the time average of these oscillations can be concentrated on TFT, favoring cooperation.

    Conclusions:

    • Stochastic evolution in finite populations can overcome the tendency for defection to dominate.
    • Cooperation can be favored even when defection is the strict Nash equilibrium.
    • Finite population dynamics offer alternative evolutionary pathways compared to infinite population models.