Arbitrage-Free Combinatorial Market Making via Integer Programming
This addresses the challenge of scaling arbitrage-free combinatorial markets for practical applications like sports betting, though it is incremental as it builds on existing methods with new computational techniques.
The paper tackles the problem of arbitrage-free pricing in combinatorial prediction markets, which is #P-hard, by proposing a new market maker using integer programming solvers via the Frank-Wolfe algorithm, and demonstrates tractability and improved accuracy on real-world data from the 2010 NCAA basketball tournament with an outcome space of size 2^63.
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.