Game theory and the sport sciences: Setting an optimal threshold level in sport competitions

This paper demonstrates the applicability of game theory to the sport sciences by analysing a specific policy making problem where an athlete has to set a threshold for entering a competition. Although the application of game theory to sport competitions seems quite straightforward, there are very few studies which actually do this. We explore the mechanism through which a player decides on the threshold of entering a two-player sport competition with one simultaneous move and both players only benefit if they end in the first place. The simplified game shows that when both players are determined to win, the game has a Pareto inferior Nash equilibrium, meaning that the two players could have improved their pay-offs had they adopted a cooperative rather than conflictual approach to sport competition.