Contests with Delegation and Initial Probabilities of Winning

We study a two-player contest in which each player is endowed with an initial probability of winning the prize and hires a delegate who expends effort on each player's behalf. We show that (i) the players' equilibrium delegation contracts are monotonic in the initial probabilities of winning and the impact parameter; (ii) the delegates' equilibrium effort levels are monotonic in the impact parameter but not in the initial probabilities of winning; and (iii) a contest designer may attain various objectives of contest design by choosing a proper value of the impact parameter