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Iterated Prisoner's Dilemma: pay-off variance

K Nishimura1, D W Stephens

  • 1Nebraska Behavioural Biology Group, School of Biological Sciences, University of Nebraska, Lincoln, NE 68588, USA. strixkn@fish.fish.kokudai.ac.jp

Journal of Theoretical Biology
|September 23, 1997
PubMed
Summary

Finite population size and payoff variance in the iterated Prisoner's Dilemma (IPD) challenge standard ESS analysis. Tit-for-tat (TFT) strategies face invasion risks from all-defect strategies (ALLD) due to payoff variance, not just mean payoffs.

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Area of Science:

  • Evolutionary Game Theory
  • Computational Biology
  • Behavioral Economics

Background:

  • The iterated Prisoner's Dilemma (IPD) is typically analyzed using arithmetic mean payoffs within an Evolutionarily Stable Strategy (ESS) framework.
  • Standard ESS analysis often overlooks factors like finite population size and the number of game iterations, which can influence strategic dynamics.

Purpose of the Study:

  • To investigate the impact of finite population size, payoff variance, and stochastic processes on the invasion dynamics of strategies in the IPD.
  • To re-evaluate the conditions under which an all-defect strategy (ALLD) can invade a population of tit-for-tat (TFT) strategists.

Main Methods:

  • Development of a general formula for the payoff variance of the Markov strategist in the IPD.
  • Analysis of the initial invasion process of ALLD into a TFT population using stochastic processes.

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  • Comparison of predictions from stochastic models with standard deterministic ESS analysis.

    • Main Results:

    • Finite population size, strategic errors, and payoff variances alter the predicted invasion dynamics of ALLD compared to standard ESS analysis.
    • While TFT may have a higher arithmetic mean payoff, its payoff variance increases with the number of game iterations.
    • The critical threshold (w) for ALLD invasion into TFT populations is found to be larger than predicted by deterministic models.

    Conclusions:

    • Payoff variance and stochastic effects are crucial for accurately modeling evolutionary dynamics in finite populations.
    • The standard ESS analysis may underestimate the resilience of TFT strategies against ALLD under certain conditions.
    • Incorporating payoff variance provides a more nuanced understanding of strategy evolution in the iterated Prisoner's Dilemma.