Evolutionarily stable strategy distributions for the Repeated Prisoner's Dilemma

Area of Science:

• Evolutionary Game Theory
• Game Theory
• Behavioral Economics

Background:

• Evolutionarily stable strategies (ESS) are key to understanding strategy persistence in evolutionary game theory.
• The standard Prisoner's Dilemma and its repeated variant are foundational models for studying cooperation and defection.
• Generalizing ESS to distributions is crucial for analyzing complex ecological and social interactions.

Purpose of the Study:

• To introduce and define the concept of an evolutionarily stable strategy distribution (ESSD).
• To apply the ESSD concept to the n-person Repeated Prisoner's Dilemma.
• To investigate the existence of ESSDs under varying conditions of mutation and interaction probability.

Main Methods:

• Formalizing the definition of an evolutionarily stable strategy distribution.
• Applying game-theoretic analysis to the n-person Repeated Prisoner's Dilemma framework.
• Investigating the impact of mutation rates and the probability of future interactions on strategy distribution stability.

Main Results:

• The study defines ESSD as a set of symbiotic strategies resilient to low mutation levels.
• For the n-person Repeated Prisoner's Dilemma, it's shown that no ESSDs exist when the probability of future interactions is sufficiently high.
• A specific example demonstrates an ESSD's existence when the set of possible mutant strategies is restricted.

Conclusions:

• The generalization of ESS to distributions provides a more robust framework for analyzing strategy stability.
• High interaction probabilities in the Repeated Prisoner's Dilemma, under standard mutation assumptions, preclude the existence of evolutionarily stable strategies.
• Further research into restricted mutation sets may yield insights into the emergence of stable cooperative strategies.