Generalize Stepwise Uncertainty Reduction to Mixed Nash Equilibria

Generalize stepwise uncertainty reduction from Bayesian optimization criteria for pure equilibria to mixed Nash equilibria in finite games, thereby providing an acquisition criterion applicable when equilibrium strategies have non-singleton supports.

Background

The paper discusses acquisition strategies for selecting expensive payoff evaluations in simulation-based games. It contrasts its bootstrap sensitivity rule with stepwise uncertainty reduction, a criterion developed for Bayesian optimization that targets uncertainty about whether a candidate strategy is an equilibrium.

The authors note that this criterion does not directly extend to the mixed equilibria considered in the paper, whose supports may contain multiple strategies. Developing such a generalization would provide a principled alternative for query-efficient Nash equilibrium computation in finite games with mixed strategies; the paper explicitly leaves this extension unresolved.