Efficient Strategy Computation in Zero-Sum Asymmetric Repeated Games

TL;DR

This paper develops efficient linear programming methods to compute approximate security strategies in finite-horizon and discounted infinite-horizon nested information zero-sum games, improving computational tractability.

Contribution

It introduces a refined sequence form and LP formulations tailored for nested information games, enabling scalable strategy computation for both players.

Findings

LP-based strategies depend only on informed player's history.

The approach provides bounds on strategy performance difference.

Illustrative example demonstrates practical effectiveness.

Abstract

Zero-sum asymmetric games model decision making scenarios involving two competing players who have different information about the game being played. A particular case is that of nested information, where one (informed) player has superior information over the other (uninformed) player. This paper considers the case of nested information in repeated zero-sum games and studies the computation of strategies for both the informed and uninformed players for finite-horizon and discounted infinite-horizon nested information games. For finite-horizon settings, we exploit that for both players, the security strategy, and also the opponent's corresponding best response depend only on the informed player's history of actions. Using this property, we refine the sequence form, and formulate an LP computation of player strategies that is linear in the size of the uninformed player's action set. For the infinite-horizon discounted game, we construct LP formulations to compute the approximated security strategies for both players, and provide a bound on the performance difference between the approximated security strategies and the security strategies. Finally, we illustrate the results on a network interdiction game between an informed system administrator and uniformed intruder.