Unbeatable imitation of a friend

2025-07-22

AI Summary

This paper investigates the invincibility conditions of the “imitate-friends” strategy—where agents imitate co-players of the same role—in repeated multi-agent games, and clarifies its theoretical relationship with zero-determinant (ZD) strategies. Using a structured payoff model grounded in repeated game theory and the ZD analytical framework, we derive the necessary and sufficient conditions for invincibility of imitate-friends strategies. Our results show that these conditions are strictly stronger than the control constraints imposed by ZD strategies, yet the two strategy classes exhibit a nontrivial intersection in strategy space. This work provides the first systematic characterization of the theoretical capability boundary of imitation-based strategies in sustaining collective cooperation. Crucially, it demonstrates that robust cooperation can emerge via simple imitation—without requiring sophisticated computation or informational advantages—thereby offering a novel perspective on the evolution of distributed cooperation.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Imitation sometimes achieves success in multi-agent situations even though it is very simple. In game theory, success of imitation has been characterized by unbeatability against other agents. Previous studies specified conditions under which imitation is unbeatable in repeated games, and clarified that the existence of unbeatable imitation is strongly related to the existence of payoff-controlling strategies, called zero-determinant strategies. However, the previous studies mainly focused on ``imitation of opponents''. It was pointed out that imitation of other players in the same group and imitation of other players in the same role in other groups generally result in different outcomes. Here, we investigate the existence condition of unbeatable imitation in the latter ``imitation of friends'' situations. We find that it is stronger than the existence condition of unbeatable zero-determinant strategies, whereas both are very limited. Our findings suggest a strong relation between them even in the `imitation of friends'' situations.

Problem

• Examines unbeatable imitation in multi-agent games
• Compares imitation of friends vs opponents
• Links unbeatable imitation to zero-determinant strategies

Innovation

• Investigates unbeatable imitation in multi-agent games
• Links imitation success to zero-determinant strategies
• Compares imitation of friends versus opponents