In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium.
In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government.
In a world where a politician can explicitly auction off a prize to the high bidder, the standard auction literature can be used to analyse political behavior. The justice system, however, precludes politicians from explicitly selling the prize to the highest bidder. Thus politicians cannot let it become public knowledge that they are in the business of selling political favors. An institution has emerged in political markets to overcome this constraint which are termed as lobbying. Lobbyists make implicit payments to the politician through campaign contributions. If these up-front payments were rebated to those failing to receive the prize, it would be clear that the politician was selling favors. This article has examined an interesting principle arising in all-pay auctions. This principle states that a politician wishing to maximize political rents may find it in his best interest to exclude certain lobbyists from participating in the lobbying process, particularly lobbyists valuing most the political prize.
