Title: Optimal thresholds in symmetric multi-stage multi-players competitions

Authors: Lea Friedman, Zilla Sinuany-Stern, Abraham Mehrez

Addresses: Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel. ' Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel and College of Judea and Samaria, PO Box 3, Ariel 44837, Israel. ' School of Management, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva, Israel

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.

Keywords: symmetric games; decision analysis; optimal threshold; multi-player games; sports.

DOI: 10.1504/IJSMM.2006.008118

International Journal of Sport Management and Marketing, 2006 Vol.1 No.3, pp.239 - 254

Published online: 17 Nov 2005 *

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