Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games

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 counterterrorism. We evaluate our main algorithm experimentally on a prototypical search game. Our results show that it performs well compared with existing well-known algorithms for solving zero-sum games that can also be used to solve search games given a best-response oracle.

The online appendix is available at https://doi.org/10.1287/opre.2019.1853.