Learning with minimal information in continuous games

TL;DR

This paper introduces a payoff-based stochastic learning process for continuous games, demonstrating convergence to Nash equilibria under various conditions despite minimal information requirements.

Contribution

It develops a novel learning process for continuous action games that requires no game knowledge and proves convergence to Nash equilibria in broad classes of such games.

Findings

Convergence to stable Nash equilibria in games with strategic complements and concave games.

Convergence often occurs in locally ordinal potential games.

Positive probability of convergence in games with isolated equilibria.

Abstract

We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous action sets. It is payoff-based and thus requires from players no sophistication and no knowledge of the game. We show that despite such limited information, players will converge to Nash in large classes of games. In particular, convergence to a Nash equilibrium which is stable is guaranteed in all games with strategic complements as well as in concave games; convergence to Nash often occurs in all locally ordinal potential games; convergence to a stable Nash occurs with positive probability in all games with isolated equilibria.