# Solving Zero-sum Games using Best Response Oracles with Applications to Search Games

## TL;DR

This paper introduces efficient algorithms for solving zero-sum games with many strategies, leveraging best response oracles, and demonstrates their effectiveness in search game applications relevant to security and counter-terrorism.

## Contribution

The paper develops algorithms that efficiently compute strategies in large zero-sum games using best response oracles, with practical applications to search games.

## Key findings

- Algorithms perform well compared to existing methods
- Effective in large strategy spaces with polynomial-time best response oracles
- Successful application to security and counter-terrorism search scenarios

## Abstract

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given mixed strategy of Player I, a best response or "approximate" best response of Player II can be found by an oracle in time polynomial in n. We then show how our algorithms may be applied to several search games with applications to security and counter-terrorism. We evaluate our main algorithm experimentally on a prototypical search game. Our results show it performs well compared to an existing, well-known algorithm for solving zero-sum games that can also be used to solve search games, given a best response oracle.