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.Comment: Published at AAAI1