Computing Best-Response Strategies in Infinite Games of Incomplete Information

TL;DR

This paper introduces an algorithm to compute best-response strategies in a broad class of infinite two-player incomplete information games, including auctions and allocation games, enabling equilibrium analysis.

Contribution

The paper presents a novel algorithm for computing best responses in infinite games with piecewise linear payoffs, extending to equilibrium computation in certain cases.

Findings

Algorithm efficiently computes best responses in various games

Can be iterated to find Bayes-Nash equilibria

Demonstrated effectiveness on multiple existing and new game models

Abstract

We describe an algorithm for computing best response strategies in a class of two-player infinite games of incomplete information, defined by payoffs piecewise linear in agents' types and actions, conditional on linear comparisons of agents' actions. We show that this class includes many well-known games including a variety of auctions and a novel allocation game. In some cases, the best-response algorithm can be iterated to compute Bayes-Nash equilibria. We demonstrate the efficiency of our approach on existing and new games.