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A Model of a General Parimutuel System: Characterizations and Equilibrium Selection

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  • Watanabe, Takahiro
  • Nonoyama, Hideyuki
  • Mori, Masao

Abstract

We formulate a model of a parimutuel system which considers a horse race with two horses. In our model, the raceholder offers a rate of his total betting revenue in the first stage. In the second stage each bettor simultaneously decides whether he bets one unit of money on one horse or he withdraws, according to his win predictions for each horse. We assume that all bettor's predictions are different and are common knowledge. We define some types of equilibria in the second stage game and give necessary and sufficient conditions for their existence. One equilibrium is a selected as a solution for the second stage game. We also define a solution for the whole game by using this result. Finally, we analyze the relation between the solution and variance for the bettor predictions.

Suggested Citation

  • Watanabe, Takahiro & Nonoyama, Hideyuki & Mori, Masao, 1994. "A Model of a General Parimutuel System: Characterizations and Equilibrium Selection," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 237-260.
    • Handle: RePEc:spr:jogath:v:23:y:1994:i:3:p:237-60
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    Cited by:

    1. Feeney, Rob & King, Stephen P., 2001. "Sequential parimutuel games," Economics Letters, Elsevier, vol. 72(2), pages 165-173, August.
    2. Koessler, Frédéric & Noussair, Charles & Ziegelmeyer, Anthony, 2008. "Parimutuel betting under asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 733-744, July.
    3. Takahiro, Watanabe, 1997. "A parimutuel system with two horses and a continuum of bettors," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 85-100, August.
    4. Frédéric Koessler & Anthony Ziegelmeyer & Marie-Hélène Broihanne, 2003. "The Favorite-Longshot Bias in Sequential Parimutuel Betting with Non-Expected Utility Players," Theory and Decision, Springer, vol. 54(3), pages 231-248, May.
    5. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.

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