Arbitrage-Free Combinatorial Market Making via Integer Programming
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.
Cite
@article{arxiv.1606.02825,
title = {Arbitrage-Free Combinatorial Market Making via Integer Programming},
author = {Christian Kroer and Miroslav Dudík and Sébastien Lahaie and Sivaraman Balakrishnan},
journal= {arXiv preprint arXiv:1606.02825},
year = {2016}
}