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.
Similar content being viewed by others
References
Aumann RJ (1976) Agreeing to disagree. Annals of Statistics 4:1236–1239
Aumann RJ (1987) Correlated equilibria as an expression of Bayesian rationality. Econometrica 55:1–18
Güth W (1985) An extensive approach to model the nuclear detterrence debate. Journal of Institutional and Theoretical Economics 141:525–538
Hausch BD, Ziemba WD, Rubinstein M (1981) Efficiency of the market for racetrack betting. Management Science 27:1435–1452
Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press
Harsanyi JC (1967/1968) Games with incomplete information played by ‘Bayesian’ players. Management Science 14:159–182, 320–334, 486–502
Harsanyi JC (1975) The tracing procedure: A Bayesian approach to defining a solution for n-person noncooperative games. International Journal of Game Theory 4:61–94
Ikebe Y, Watanabe T (1992) An algorithm for finding all equilibria in model of a parimutuel system. Forthcoming to Asian Pacific Journal of Operations Research
Perry A, Soland RM (1975) Optimal operation of public lotteries. Management Science 22:461–469
Philips L, Harstad RM (1991) Interaction between resource extraction and futures markets: A game-theoric analysis. In: Selten R (ed) Game Equilibrium Models II 289–307 Springer Verlag
Selten R, Güth W (1982) Equilibrium point selection in a class of market entry games. In: Deistler M et al (ed) Games economics dynamics, and time series analysis — A symposium in memorium Oskar Morgenstern 101–116
Snyder WW (1978) Horse racing: Testing the efficient market model. J Finance 33:1109–1118
Vassilakis S, Zamir S (1992) Common belief and common knowledge. Mimeo
Author information
Authors and Affiliations
Additional information
We thank to Prof. Okada, A. and Ikebe, Y. for helpful discussions. Special thanks are due to an anonymous referee for very grateful comments.
Rights and permissions
About this article
Cite this article
Watanabe, T., Nonoyama, H. & Mori, M. A model of a general parimutuel system: Characterizations and equilibrium selection. Int J Game Theory 23, 237–260 (1994). https://doi.org/10.1007/BF01247317
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01247317