Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead

TL;DR

This paper introduces robust Stackelberg equilibria in extensive-form games to handle uncertainty about opponents' payoffs and limited lookahead, providing computational methods for these complex scenarios.

Contribution

It develops a new mixed-integer programming approach for computing robust Stackelberg equilibria under uncertainty and limited lookahead in extensive-form games.

Findings

Robust equilibria can be computed with mixed-integer programs of similar size to deterministic cases.

The approach handles interval uncertainty in payoffs and node evaluations.

The methods extend existing models to more realistic, uncertain strategic settings.

Abstract

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding the model about the opponent. This paper is, to our knowledge, the first to investigate Stackelberg equilibria under uncertainty in extensive-form games, one of the broadest classes of game. We introduce robust Stackelberg equilibria, where the uncertainty is about the opponent's payoffs, as well as ones where the opponent has limited lookahead and the uncertainty is about the opponent's node evaluation function. We develop a new mixed-integer program for the deterministic limited-lookahead setting. We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent. We show that for the specific case of interval uncertainty about the opponent's payoffs (or about the opponent's node evaluations in the case of limited lookahead), robust Stackelberg equilibria can be computed with a mixed-integer program that is of the same asymptotic size as that for the deterministic setting.