Optimal Favoritism in All-Pay Auctions and Lottery Contests

We analyze the revenue-enhancing potential of favoring specific contestants in complete-information all-pay auctions and lottery contests with several heterogeneous contestants. Two instruments of favoritism are considered: head starts that are added to the bids of specific contestants and multiplicative biases that give idiosyncratic weights to the bids. In the all-pay auction, head starts are more effective than biases while optimally combining both instruments even yields first-best revenue. In the lottery contest, head starts are less effective than biases and combining both instruments cannot further increase revenue. As all-pay auctions revenue-dominate lottery contests under optimal biases, we thus obtain an unambiguous revenue-ranking of all six combinations of contest formats and instruments.