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A Utility Framework for Bounded-Loss Market Makers

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  • Yiling Chen
  • David M Pennock

Abstract

We introduce a class of utility-based market makers that always accept orders at their risk-neutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk aversion utility market makers are equivalent to weighted pseudospherical scoring rule market makers. In particular, Hanson's logarithmic scoring rule market maker corresponds to a negative exponential utility market maker in our framework. We describe a third equivalent formulation based on maintaining a cost function that seems most natural for implementation purposes, and we illustrate how to translate among the three equivalent formulations. We examine the tradeoff between the market's liquidity and the market maker's worst-case loss. For a fixed bound on worst-case loss, some market makers exhibit greater liquidity near uniform prices and some exhibit greater liquidity near extreme prices, but no market maker can exhibit uniformly greater liquidity in all regimes. For a fixed minimum liquidity level, we give the lower bound of market maker's worst-case loss under some regularity conditions.

Suggested Citation

  • Yiling Chen & David M Pennock, 2012. "A Utility Framework for Bounded-Loss Market Makers," Papers 1206.5252, arXiv.org.
  • Handle: RePEc:arx:papers:1206.5252
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    File URL: http://arxiv.org/pdf/1206.5252
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    References listed on IDEAS

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    1. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    2. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    3. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
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    Cited by:

    1. Razvan Tarnaud, 2019. "Convergence within binary market scoring rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 1017-1050, November.
    2. Hamed Amini & Maxim Bichuch & Zachary Feinstein, 2023. "Decentralized Prediction Markets and Sports Books," Papers 2307.08768, arXiv.org, revised May 2024.
    3. Yuqing Kong & Grant Schoenebeck, 2022. "False Consensus, Information Theory, and Prediction Markets," Papers 2206.02993, arXiv.org, revised Nov 2022.
    4. Dian Yu & Jianjun Gao & Weiping Wu & Zizhuo Wang, 2022. "Price Interpretability of Prediction Markets: A Convergence Analysis," Papers 2205.08913, arXiv.org, revised Nov 2023.
    5. Siddarth Srinivasan & Ezra Karger & Yiling Chen, 2023. "Self-Resolving Prediction Markets for Unverifiable Outcomes," Papers 2306.04305, arXiv.org.

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