Forgiver triumphs in alternating Prisoner's Dilemma

Area of Science:

• Evolutionary Game Theory
• Behavioral Economics
• Computational Social Science

Background:

• Cooperative behavior, involving personal cost for mutual benefit, is prevalent.
• Direct reciprocity in the alternating Prisoner's Dilemma is a key model for studying cooperation.

Purpose of the Study:

• To analyze strategies for direct reciprocity in the Prisoner's Dilemma with noise.
• To identify conditions favoring stable cooperation through specific strategies.

Main Methods:

• Examined strategies implementable by one and two-state automata.
• Calculated payoff matrices for pairwise encounters with noise.
• Explored deterministic selection dynamics with and without mutation.

Main Results:

• Observed convergence to equilibria, including uncooperative (ALLD, Grim) and a mixed cooperative alliance.
• Identified the

Conclusions:

• Forgiveness, exemplified by the "Forgiver" strategy, facilitates stable cooperation.
• While not evolutionarily stable itself, the cooperative alliance it leads is asymptotically stable.
• Forgiveness can lead to long-term gains by enabling cooperation despite exploitation and noise.