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Mistakes allow evolutionary stability in the repeated prisoner's dilemma game
1Department of Anthropology, University of California, Los Angeles, 90024.
Journal of Theoretical Biology
|January 9, 1989
Summary
Mistakes in the repeated prisoner's dilemma allow pure strategies like unconditional defection or modified tit-for-tat to be evolutionarily stable. These strategies are robust best responses to themselves, even with errors.
Area of Science:
- Evolutionary game theory
- Behavioral economics
- Game theory
Background:
- The repeated prisoner's dilemma is a key model for studying reciprocal altruism.
- Previous research indicated no pure strategy could be evolutionarily stable in this game.
Purpose of the Study:
- To investigate if errors can lead to evolutionarily stable pure strategies in the repeated prisoner's dilemma.
- To identify conditions under which pure strategies can be robust in evolutionary game theory.
Main Methods:
- Analysis of evolutionary stability in the repeated prisoner's dilemma with probabilistic errors.
- Definition and application of "strong perfect equilibria" to strategy evaluation.
- Examination of unconditional defection and a modified tit-for-tat strategy.
Main Results:
- A pure strategy can be evolutionarily stable if errors are present.
- Strategies must be "strong perfect equilibria" against themselves to achieve stability.
- Both unconditional defection and a modified tit-for-tat satisfy this condition.
Conclusions:
- Introducing errors into the repeated prisoner's dilemma can stabilize pure strategies.
- The concept of "strong perfect equilibria" is crucial for understanding strategy stability with errors.
- This finding has implications for the evolution of cooperation and altruism.