Learning with Episodic Hypothesis Testing in General Games: A Framework for Equilibrium Selection

TL;DR

This paper proposes a hypothesis testing-based learning framework for general games that converges to equilibria, especially those maximizing minimum utility, offering a new approach to equilibrium selection.

Contribution

It introduces a novel learning dynamics combining hypothesis testing with utility-driven exploration, leading to convergence to refined equilibria in finite games.

Findings

Converges to approximate Nash equilibria.

Selects equilibria maximizing minimum utility.

Provides a new mechanism for equilibrium refinement.

Abstract

We introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies and episodically tests these beliefs using empirical observations. Beliefs are resampled either when the hypothesis test is rejected or through exploration, where the probability of exploration decreases with the player's (transformed) utility. In general finite normal-form games, we show that the learning process converges to a set of approximate Nash equilibria and, more importantly, to a refinement that selects equilibria maximizing the minimum (transformed) utility across all players. Our result establishes convergence to equilibrium in general finite games and reveals a novel mechanism for equilibrium selection induced by the structure of the learning dynamics.