Arbitrage-Free Combinatorial Market Making via Integer Programming

TL;DR

This paper introduces a novel arbitrage-free combinatorial market maker using integer programming and the Frank-Wolfe algorithm, demonstrating its effectiveness on large-scale real-world prediction data.

Contribution

It presents the first scalable implementation of an arbitrage-free combinatorial prediction market leveraging integer programming and the Frank-Wolfe algorithm.

Findings

Successfully applied to NCAA tournament data with 2^63 outcome space

Demonstrated improved accuracy and tractability over existing methods

First empirical evaluation of such a market on this scale

Abstract

We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs. Although the problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by the market maker, is #P-hard in the worst case, we posit that the typical case might be amenable to modern integer programming (IP) solvers. At the crux of our method is the Frank-Wolfe (conditional gradient) algorithm which is used to implement a Bregman projection aligned with the market maker's cost function, using an IP solver as an oracle. We demonstrate the tractability and improved accuracy of our approach on real-world prediction market data from combinatorial bets placed on the 2010 NCAA Men's Division I Basketball Tournament, where the outcome space is of size 2^63. To our knowledge, this is the first implementation and empirical evaluation of an arbitrage-free combinatorial prediction market on this scale.