Seven rules to avoid the tragedy of the commons

Area of Science:

• Game Theory
• Behavioral Economics
• Computational Social Science

Background:

• Social dilemmas, like the public goods game, often fail due to self-interested agents and implementation errors.
• Achieving stable cooperation that benefits all players is a significant challenge in repeated interactions.
• Existing strategies may not guarantee protection against exploitation when errors occur.

Purpose of the Study:

• To identify a strategy for the repeated n-person public-goods game that establishes a cooperative Nash equilibrium.
• To ensure the chosen strategy guarantees payoffs no less than any co-player's, even with implementation errors.
• To determine the minimum memory length required for such a stabilizing strategy.

Main Methods:

• Analysis of the repeated n-person public-goods game with implementation errors.
• Enumeration of strategic possibilities for a specific case (n=3).
• Mathematical determination of necessary conditions for strategy effectiveness.

Main Results:

• A deterministic strategy with memory length m=3 was found to stabilize cooperation for n=3 players.
• This strategy ensures a cooperative Nash equilibrium and prevents exploitation despite errors.
• For general n-person games, a memory length of m ≥ n is necessary to meet the criteria.

Conclusions:

• Cooperation in social dilemmas can be stabilized against errors using deterministic strategies with sufficient memory.
• The findings provide a theoretical basis for designing robust cooperative mechanisms in multi-agent systems.
• The required memory length increases with the number of players, highlighting scalability considerations.