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Gaming Prediction Markets: Equilibrium Strategies with a Market Maker

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Abstract

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for the infinite-stage market with discounting, the market price converges to the fully-revealing price, and the rate of convergence can be bounded in terms of the discounting parameter. When signals are conditionally independent, truthful betting is the unique WPBE for the infinite-stage market with and without discounting.

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Authors and Affiliations

  1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Yiling Chen

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA

    Stanko Dimitrov

  3. School of Information, University of Michigan, Ann Arbor, MI, USA

    Rahul Sami

  4. Yahoo! Research, New York, NY, USA

    Daniel M. Reeves & David M. Pennock

  5. Department of Economics, George Mason University, Fairfax, VA, USA

    Robin D. Hanson

  6. EECS Department, Northwestern University, Evanston, IL, USA

    Lance Fortnow

  7. Yahoo! Research, Santa Clara, CA, USA

    Rica Gonen

Authors
  1. Yiling Chen
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  2. Stanko Dimitrov
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  3. Rahul Sami
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  4. Daniel M. Reeves
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  5. David M. Pennock
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  6. Robin D. Hanson
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  7. Lance Fortnow
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  8. Rica Gonen
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Corresponding author

Correspondence to Yiling Chen.

Additional information

Preliminary versions of some of the results in this paper were presented in two conference papers, Chen et al. [10] and Dimitrov and Sami [13].

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Chen, Y., Dimitrov, S., Sami, R. et al. Gaming Prediction Markets: Equilibrium Strategies with a Market Maker. Algorithmica 58, 930–969 (2010). https://doi.org/10.1007/s00453-009-9323-2

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  • DOI: https://doi.org/10.1007/s00453-009-9323-2

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