Essays on Auction Theory

This work is composed of three essays on auction theory. In the first essay, we analyze the optimal auction of multiple non-identical objects when buyers are risk averse. We show that the auction forms that yield the maximum revenue in the risk neutral case are no longer optimal. In particular, selling the goods independently does not maximize the seller's revenue. On the other hand, the optimal auction remains weakly efficient. The optimal auction has the following properties: The seller perfectly insures all buyers against the risk of losing the object(s) for which they have high valuation. While the buyers who have high valuation for both objects are compensated if they do not win either object, the buyers who have low valuation for both objects incur a positive payment in the same event.In the second essay, we question whether, in the all-pay auction, the seller's commitment to the reserve price is beneficial if she has the chance of repeating the auction, possibly with a different reserve price, in case there is no sale in the first period. We show that, for any number of potential buyers, non-commitment is preferable only if the seller is relatively more patient than the buyers. Moreover, as the number of potential buyers increases, the seller's incentive to commit increases if she maximizes the average bid, whereas it decreases if she maximizes the highest bid. A possible explanation is that if the seller maximizes the average (highest) bid then screening high types (highest type) becomes costlier (less costly) as more buyers participate in the auction.The third essay studies collusive behavior in the Ausubel auction in an environment with incomplete information. The Ausubel auction is vulnerable to collusion due to two main reasons: First, the mechanism has a dynamic nature that allows the bidders to detect and punish those that deviate from the agreed collusive strategy. Second, in case a bidder strategically reduces his demand to signal his intention to collude, the mechanism allows the opponents to correctly interpret the signal