THREE ESSAYS ON AUCTION THEORY AND CONTEST THEORY

In the first chapter, ¡°All-Pay Auctions with Resale¡±, I study equilibria of first- and second-price all-pay auctions with resale when players' signals are affiliated and symmetrically distributed. I show that existence of resale possibilities introduces an endogenous element to players' valuations and creates a signaling incentive for players. I characterize symmetric bidding equilibria for both first- and second-price all-pay auctions with resale and provide sufficient conditions for existence of symmetric equilibria. Under those conditions I show that second-price all-pay auctions generate no less expected revenue than first-price all-pay auctions with resale. The initial seller could benefit from publicly disclosing her private information which is affiliated with players' signals.Outcome in all-pay auctions is deterministic since the highest bidder wins the prize with probability one. However, many realistic contests have in-deterministic outcome and no player can guarantee winning the prize. The second chapter, ¡°Rent-Seeking Contest with Private Values and Resale¡±, studies rent-seeking contests with private values and resale possibilities. With an in-deterministic success function, the resulting possible inefficiency creates a motive for aftermarket trade. Players' valuations are endogenously determined when there is an opportunity of resale. I characterize symmetric equilibria. I assume that the winner has full bargaining power; however, the results extend to other resale mechanisms. I show that resale enhances allocative efficiency ex post at the expense of more wasted social resources since players compete more aggressively with resale possibilities.In the third chapter, ¡°The Imperfectly Discriminating Contests with Incomplete Information¡±, I study the existence of monotone pure-strategy equilibria in imperfectly discriminating contests with incomplete information. Sufficient conditions under which equilibria exist are provided for both finite-action and continuum-action cases. Using a two-bidder example, we derive some properties of equilibria and show a special case of revenue equivalence between contests with incomplete information and contests with complete information.