Double Oracle Algorithm for Computing Equilibria in Continuous Games

TL;DR

This paper introduces a double oracle algorithm for efficiently computing Nash equilibria in continuous two-player zero-sum games with compact strategy sets, extending iterative methods to infinite strategy spaces.

Contribution

It develops and proves convergence of a novel iterative double oracle algorithm applicable to a broad class of continuous games, including those not solvable by semidefinite programming.

Findings

Algorithm converges to Nash equilibrium

Outperforms fictitious play in experiments

Effective on continuous Colonel Blotto game

Abstract

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.