Learning Cooperative Games

TL;DR

This paper investigates the PAC learnability of various cooperative game classes from samples and links learnability to core stability, enabling stable payoff predictions with limited data.

Contribution

It introduces a PAC learning framework for cooperative games and connects it to core stability, providing new insights into learnability and stability in game theory.

Findings

PAC learnability established for network flow, threshold task, and induced subgraph games

Efficient learnability implies the possibility of finding likely stable payoff divisions

Polynomial sample complexity suffices for stable payoff predictions

Abstract

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.