Optimal thresholds in symmetric multi-stage multi-players competitions
by Lea Friedman, Zilla Sinuany-Stern, Abraham Mehrez
International Journal of Sport Management and Marketing (IJSMM), Vol. 1, No. 3, 2006

Abstract: In this paper we deal with symmetric multi-stage multi-players games where the optimal threshold has to be determined for maximising the expected reward. These types of competitions are common in sport games, e.g., high jump and weightlifting. We derive the optimal solution for intermediate stages. For the final stage we do not have a closed-form solution for the general case; however, we only have first and second order conditions for optimality. Nevertheless, we develop closed-form solutions for several special cases.

Online publication date: Thu, 17-Nov-2005

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