Double-oracle sampling method for Stackelberg Equilibrium approximation in general-sum extensive-form games

TL;DR

This paper introduces a generic Monte Carlo Tree Search-based method for approximating Strong Stackelberg Equilibrium in complex sequential games, demonstrating superior scalability and efficiency over existing optimization techniques.

Contribution

It proposes a novel iterative sampling approach that does not depend on specific game properties, improving approximation of equilibrium strategies in general-sum extensive-form games.

Findings

Achieves near-optimal Leader strategies in most test cases.

Outperforms state-of-the-art MILP/LP methods in time and memory efficiency.

Effective in diverse interception game scenarios.

Abstract

The paper presents a new method for approximating Strong Stackelberg Equilibrium in general-sum sequential games with imperfect information and perfect recall. The proposed approach is generic as it does not rely on any specific properties of a particular game model. The method is based on iterative interleaving of the two following phases: (1) guided Monte Carlo Tree Search sampling of the Follower's strategy space and (2) building the Leader's behavior strategy tree for which the sampled Follower's strategy is an optimal response. The above solution scheme is evaluated with respect to expected Leader's utility and time requirements on three sets of interception games with variable characteristics, played on graphs. A comparison with three state-of-the-art MILP/LP-based methods shows that in vast majority of test cases proposed simulation-based approach leads to optimal Leader's strategies, while excelling the competitive methods in terms of better time scalability and lower memory requirements.