Arbitration supports reciprocity when there are frequent perception errors

Area of Science:

• Behavioral Economics
• Game Theory
• Evolutionary Biology

Background:

• Reciprocity is crucial for cooperation but is often disrupted by perception errors, leading to disagreements about past actions.
• Existing strategies like win-stay-lose-shift and generous tit-for-tat can restore cooperation but are ineffective when errors are frequent.

Purpose of the Study:

• To introduce and analyze a novel strategy, arbitration tit-for-tat (ATFT), designed to overcome perception errors in reciprocal interactions.
• To determine the conditions under which ATFT is evolutionarily stable and can establish cooperation despite frequent disagreements.

Main Methods:

• Developed a game-theoretic model incorporating third-party arbitration to resolve perception errors.
• Analyzed ATFT's stability as a subgame-perfect equilibrium and its evolutionary stability against various competing strategies.
• Simulated ATFT's persistence under conditions of frequent errors, costly arbitration, and biased arbitration.

Main Results:

• ATFT is a strong subgame-perfect equilibrium when arbitration is moderately accurate.
• ATFT is evolutionarily stable against defectors, unconditional cooperators, and strategies that misuse arbitration.
• ATFT can persist even with frequent perception errors, high arbitration costs, or biased arbitration.

Conclusions:

• Third-party arbitration provides a robust mechanism for maintaining reciprocity when perception errors are common.
• The findings suggest a potential explanation for the rarity of reciprocity in non-human animals and the role of social norms in human cooperation.
• ATFT offers a framework for understanding how social institutions can support cooperation in complex environments.