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ParlayMarket: Automated Market Making for Parlay-Style Joint Contracts

Authors Ranvir Rana , Viraj Nadkarni , Niusha Moshrefi, Pramod Viswanath

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LIPIcs.AFT.2026.15.pdf
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ACM Subject Classification
  • Theory of computation → Market equilibria
  • Theory of computation → Online learning theory
  • Applied computing → Economics
Keywords
  • Prediction markets
  • automated market makers
  • parlays
  • market scoring rules
  • online learning

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Abstract

Prediction markets are powerful mechanisms for information aggregation, but existing designs are optimized for single-event contracts. Traders frequently express beliefs about joint outcomes - sports parlays, conditional forecasts, multi-scenario financial bets. Current platforms either prohibit such trades or rely on ad hoc mechanisms that ignore correlation structure, resulting in inefficient prices and fragmented liquidity. We introduce ParlayMarket, an automated market-maker for parlay-style joint contracts. The mechanism maintains a shared pairwise exponential-family belief state, so all base and parlay prices are marginals of one coherent distribution. This compresses the 2^M outcome space into O(M²) sufficient statistics and allows one liquidity pool to support an exponentially large family. Our main result characterizes the resulting learning and loss dynamics. Under repeated trading, prices converge to the best pairwise approximation of the true joint distribution. The induced expected market-maker loss grows at most quadratically in the number of base events, rather than exponentially in the number of listed parlays; moreover, this quadratic dependence is worst-case optimal for dense pairwise dependence, since there are O(M²) independent correlation directions to learn. Parlay trades are essential to this guarantee: they provide direct constraints on joint outcomes and reduce steady-state error relative to learning from marginal trades alone. Experiments on synthetic correlated markets and historical Kalshi combo data confirm the predicted scaling and show that the mechanism remains effective in realistic market-making settings. Our results demonstrate that combinatorial expressiveness does not require combinatorial capital.

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Ranvir Rana, Viraj Nadkarni, Niusha Moshrefi, and Pramod Viswanath. ParlayMarket: Automated Market Making for Parlay-Style Joint Contracts. In 8th Conference on Advances in Financial Technologies (AFT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 395, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AFT.2026.15

Author Details

Ranvir Rana
  • Kaleidoscope Blockchain Inc., Raleigh, NC, USA
Viraj Nadkarni
  • Princeton University, NJ, USA
Niusha Moshrefi
  • Princeton University, NJ, USA
Pramod Viswanath
  • Princeton University, NJ, USA

References

  1. Jacob Abernethy, Yiling Chen, and Jennifer Wortman Vaughan. Efficient market making via convex optimization. In ACM EC, 2013. Google Scholar
  2. Jacob Abernethy, Sindhu Kutty, Sébastien Lahaie, and Rahul Sami. Information aggregation in exponential family markets. In Proceedings of the 15th ACM Conference on Economics and Computation (EC), 2014. Google Scholar
  3. Guillermo Angeris, Tarun Chitra, Alex Evans, and Stephen Boyd. Improved price oracles: Constant function market makers. Proceedings of the 2nd ACM Conference on Advances in Financial Technologies, 2020. URL: https://arxiv.org/abs/2003.10001.
  4. Julian Besag. Statistical analysis of non-lattice data. The Statistician, 24(3):179-195, 1975. Google Scholar
  5. Guy Bresler. Efficiently learning ising models on arbitrary graphs. In Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, 2015. URL: https://doi.org/10.1145/2746539.2746631.
  6. Yiling Chen, Nicolas Lambert, David M. Pennock, and Jennifer Wortman Vaughan. Eliciting predictions and recommendations for decision making. ACM Transactions on Embedded Computing Systems, 9(4):39:1-39:21, 2010. URL: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/04/TEAC-final1.pdf.
  7. Yiling Chen and David M. Pennock. A utility framework for bounded-loss market makers. Journal of Artificial Intelligence Research, 2007. Google Scholar
  8. Yiling Chen, David M. Pennock, Michael H. Bowling, and Nicolas Lambert. Price updating in combinatorial prediction markets with bayesian networks. In Proceedings of the 23rd AAAI Conference on Artificial Intelligence, 2008. URL: https://arxiv.org/abs/1202.3756.
  9. Free Systems. Building the truth machine. https://open.substack.com/pub/freesystems/p/building-the-truth-machine, 2024. Substack.
  10. Rafael Frongillo, Ian Kash, and Mark D. Reid. Interpreting prediction markets: A stochastic approach. In Advances in Neural Information Processing Systems, 2012. URL: https://papers.nips.cc/paper/4529-interpreting-prediction-markets-a-stochastic-approach.
  11. Robin Hanson. Logarithmic market scoring rules for modular combinatorial information aggregation. Technical report, George Mason University, 2002. Google Scholar
  12. Robin Hanson. Combinatorial information market design. Information Systems Frontiers, 5(1):107-119, 2003. URL: https://doi.org/10.1023/A:1022058209073.
  13. Robin Hanson. Logarithmic market scoring rules for modular combinatorial information aggregation. Journal of Prediction Markets, 2007. Google Scholar
  14. Elad Hazan. Introduction to Online Convex Optimization. Now Publishers, 2019. URL: https://arxiv.org/abs/1909.05207.
  15. Sharif Hossain, Jenn Wortman Vaughan, Yuan Wang, and Yiling Chen. Designing automated market makers for combinatorial securities: A geometric viewpoint. In Proceedings of the 13th ACM Conference on Economics and Computation (EC), 2012. Google Scholar
  16. Kalshi. Kalshi: Event contracts exchange. https://kalshi.com, 2024. Accessed: 2026-03-19.
  17. Kathryn Blackmond Laskey, Tai Sing Lee, Robin Hanson, Charles Twardy, Shun-Yang Matsumoto, and Brandon Goldfedder. Graphical model market maker for combinatorial prediction markets. In Proceedings of the AAAI Workshop on Trading Agent Design and Analysis, 2012. Google Scholar
  18. Bruce G. Lindsay. Composite likelihood methods. In N. U. Prabhu, editor, Statistical Inference from Stochastic Processes, volume 80 of Contemporary Mathematics, pages 221-239. American Mathematical Society, Providence, RI, 1988. Google Scholar
  19. Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden, and Anthony Lee Zhang. Automated market making and loss-versus-rebalancing. arXiv preprint, 2022. URL: https://arxiv.org/abs/2208.06046.
  20. Abraham Othman and Tuomas Sandholm. When do markets with simple traders fail? In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2010. URL: https://www.ifaamas.org/Proceedings/aamas2010/pdf/01%20Full%20Papers/18_02_FP_0266.pdf.
  21. Polymarket. Polymarket: A decentralized information market platform. https://polymarket.com, 2024. Accessed: 2026-03-19.
  22. Pradeep Ravikumar, Martin J. Wainwright, and John D. Lafferty. High-dimensional ising model selection using 𝓁₁-regularized logistic regression. The Annals of Statistics, 38(3):1287-1319, 2010. URL: https://doi.org/10.1214/09-AOS691.
  23. Dan Robinson and Ciamac C. Moallemi. pm-amm. https://www.paradigm.xyz/2024/11/pm-amm, 2024.
  24. Marc Vuffray, Sidhant Misra, Andrey Y. Lokhov, and Michael Chertkov. Interaction screening: Efficient and sample-optimal learning of ising models. In Advances in Neural Information Processing Systems, 2016. URL: https://arxiv.org/abs/1605.07252.
  25. Martin J. Wainwright and Michael I. Jordan. Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning, 1(1-2):1-305, 2008. URL: https://doi.org/10.1561/2200000001.
  26. Martin Zinkevich. Online convex programming and generalized infinitesimal gradient ascent. In Proceedings of the 20th International Conference on Machine Learning (ICML), 2003. URL: https://www.cs.cmu.edu/~maz/publications/techconvex.pdf.
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