On the Impossibility of Learning to Cooperate with Adaptive Partner Strategies in Repeated Games

TL;DR

This paper proves that it is impossible for any learning algorithm to reliably cooperate with all possible adaptive partners in repeated games, highlighting fundamental limitations in learning to cooperate with evolving agents.

Contribution

The paper establishes impossibility results showing the fundamental limits of learning to cooperate with adaptive agents in repeated games, without restrictive assumptions.

Findings

No algorithm can reliably learn to cooperate with all adaptive partners.

Impossibility holds even if the partner is guaranteed to cooperate with some stationary strategy.

Discussion of alternative assumptions for rational adaptation.

Abstract

Learning to cooperate with other agents is challenging when those agents also possess the ability to adapt to our own behavior. Practical and theoretical approaches to learning in cooperative settings typically assume that other agents' behaviors are stationary, or else make very specific assumptions about other agents' learning processes. The goal of this work is to understand whether we can reliably learn to cooperate with other agents without such restrictive assumptions, which are unlikely to hold in real-world applications. Our main contribution is a set of impossibility results, which show that no learning algorithm can reliably learn to cooperate with all possible adaptive partners in a repeated matrix game, even if that partner is guaranteed to cooperate with some stationary strategy. Motivated by these results, we then discuss potential alternative assumptions which capture the idea that an adaptive partner will only adapt rationally to our behavior.