Invertibility of the Lottery Equilibrium

Auction theorists have long recognized that allocation mechanisms differ not only in outcomes but also in the information they reveal. Revelation of a winner’s valuation, for example, may affect subsequent dealings with lenders, suppliers, regulators, labor unions, and other third parties. We examine the analogous question for the lottery contest with complete information and asymmetric values, in which a prize is awarded probabilistically on the basis of contestants’ efforts. We show that the equilibrium effort profile uniquely identifies the valuations of all active contestants. If information revelation to third parties carries economic consequences in contest environments, this transparency may itself have implications for equilibrium behavior.