A tractable combinatorial market maker using constraint generation

Dudík, Miroslav; Lahaie, Sébastien; Pennock, David M.

doi:10.1145/2229012.2229047

Cited by 12 publications

(26 citation statements)

References 13 publications

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“…Researchers are eager to learn about the relationships between states in the same way that they are interested in to know the relationships between economic indicators or product launches. The underlying problem is NP-hard, and while new approximation techniques (Dudik et al, 2012;Lahaie et al, 2013) are possible, they may be too new for commercial adoption. On the other hand, for smaller outcomes spaces on the order of hundreds or thousands, we do not see serious technical barriers to adopting linear programming in the exchange.…”

Section: Discussionmentioning

confidence: 99%

“…In this case, limiting the expressiveness of bids (i.e., restricting what bundles are allowed) can recover tractable algorithms, though often the limits are severe and impractical (Agrawal et al, 2008;Chen et al, 2007;Chen et al, 2008a;Chen et al, 2008b;Guo and Pennock, 2009;Pennock and Xia, 2011). Alternatively, approximation schemes are possible, both stochastic (Chen et al, 2008b) and deterministic (Dudik et al, 2012;Lahaie et al, 2013).…”

Section: Designing Better Prediction Marketsmentioning

confidence: 99%

“…When the number of mutually exclusive outcomes is reasonable, in the hundreds or thousands, linear programming is a fast, reliable, and well-understood procedure and there is almost no disadvantage to adopting it. When the number of outcomes is exponential, for example 2 51 or 2 quadrillion state-by-state election outcomes, the computational complexity of linear programming (or any market mechanism) becomes intractable, though approximation schemes are possible (Dudik et al, 2012;Chen et al, 2008b;Lahaie et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

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The extent of price misalignment in prediction markets

Rothschild

Pennock

2014

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We study misaligned prices for logically related contracts in prediction markets. First, we uncover persistent arbitrage opportunities for risk-neutral investors between identical contracts on different exchanges. Examining the impact of several thousand dollars of transactions on the exchanges themselves in a randomized field trial, we document that price support extends well beyond what is seen in the published order book and that arbitrage opportunities are significantly larger than purely observational measurements indicate. Second, we demonstrate misalignment among identical and logically related contracts listed on the same exchange that cluster around moments of high information flow, when related contracts systemically shut down or fail to respond efficiently. Third, we document bounded rationality in prediction markets; examples include: consistent asymmetry between buying and selling, leaving the average return for selling higher than for buying; and persistent price lags between exchanges. Despite these signs of departure from theoretical optimality, the markets studied function well on balance, considering the sometimes complex and subtle relationships among contracts. Yet, we detail how to improve prediction markets by moving the burden of finding and fixing logical contradictions into the exchange and providing flexible trading interfaces, both of which free traders to focus on providing meaningful information in the form they find most natural.

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Section: Discussionmentioning

confidence: 99%

Section: Designing Better Prediction Marketsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The extent of price misalignment in prediction markets

Rothschild

Pennock

2014

Self Cite

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“…Li et al (2013) extended this framework to a parameterized class of markets with adaptive liquidity, and studied the relationship of market parameters to the market's ability to aggregate information and make a profit. Dudík et al (2012) proposed a market maker that achieves some information sharing among related securities, without restricting the securities that can be traded. Convex optimization and constraint generation are used to detect and eliminate some kinds of arbitrage opportunities.…”

Section: Combinatorial Prediction Marketsmentioning

confidence: 99%

Graphical Model Market Maker for Combinatorial Prediction Markets

Laskey¹,

Sun²,

Hanson³

et al. 2018

jair

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We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

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“…For instance, the NCAA 2010 market included securities on events "Duke wins more games than Cornell" and "a team from the Big East conference wins the championship" as well as many others. Because of the large number of securities in combinatorial markets, there may be no sellers interested in trading with a given buyer, IP constraints of FWMM can be used directly in LCMM, as linear-programming relaxations, but they are usually too loose, so tighter constraints need to be derived ad hoc for each new security type, sometimes using involved combinatorial reasoning [Dudík et al 2012[Dudík et al , 2013. Since LCMM updates are usually substantially faster than solving an IP, the arbitrage-removal steps of LCMM and FWMM can be interleaved, and the more expensive projection step of FWMM should be invoked only after LCMM cannot remove much arbitrage.…”

Section: Introductionmentioning

confidence: 99%

Arbitrage-Free Combinatorial Market Making via Integer Programming

Kroer

Dudík

Lahaie

et al. 2016

Proceedings of the 2016 ACM Conference on Economics and Computation

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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

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A tractable combinatorial market maker using constraint generation

Cited by 12 publications

References 13 publications

The extent of price misalignment in prediction markets

The extent of price misalignment in prediction markets

Graphical Model Market Maker for Combinatorial Prediction Markets

Arbitrage-Free Combinatorial Market Making via Integer Programming

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