A Contest Success Function Allowing for Ties with an Application to Soccer

We generalize the Tullock Contest Success Function to allow for ties by introducing a tie-proneness parameter to account for the degree of the importance of ties in the contest. The probability of a tie reaches a maximum when the contestants provide similar efforts and it is increasing in the effort of a player if that player is relatively weak in the contest, and decreasing otherwise. We find that in the symmetric Nash-Counot equilibrium of the game induced by the contest, the equilibrium efforts do not depend on the value of the prize of the tie. Moreover, the equilibrium efforts are not necessarily monotonic with respect to the tie-proneness parameter. We test the fit of the Contest Success Function using data from the Spanish “Primera División” soccer league