The logic of contrition

Area of Science:

• Game Theory
• Evolutionary Game Theory
• Computational Game Theory

Background:

• The Repeated Prisoner's Dilemma (RPD) is a fundamental model in game theory.
• Contrite Tit For Tat (CTFT) is a highly successful RPD strategy, excelling against defectors and robust to implementation errors.
• However, CTFT is susceptible to perception errors.

Purpose of the Study:

• To analyze the performance of Contrite Tit For Tat (CTFT) against other strategies like Pavlov and Remorse.
• To investigate the robustness of CTFT and related strategies within an eight-dimensional space of stochastic strategies.
• To develop an evolutionarily stable strategy (ESS) immune to perception and implementation errors.

Main Methods:

• Analytical investigation of stochastic strategies.
• Numerical simulations within an eight-dimensional strategy space.
• Comparison of CTFT, Pavlov, Remorse, and a novel strategy, Prudent Pavlov.

Main Results:

• CTFT demonstrates strong performance against defectors and is robust to implementation errors.
• CTFT's vulnerability to perception errors was confirmed.
• A new strategy, Prudent Pavlov, was developed, proving immune to both mis-perception and mis-implementation.

Conclusions:

• While CTFT is effective, its perceptual vulnerability limits its universal applicability.
• Prudent Pavlov offers a more robust and evolutionarily stable strategy by modifying conventional 'standing' rules.
• The study highlights the importance of error resilience in developing effective strategies for the Repeated Prisoner's Dilemma.