Auction theory and a note on game mechanisms

This paper will review important topics on the subject of auction theory and mechanism design, these include: efficiency first and foremost, also revenue comparison between different types of auctions and the issue of incentive compatibility, individual rationality with the general idea and proof that bilateral trade is inefficient. Mechanism design theory tells us that if buyers and sellers both have private information full efficiency is impossible, however Vickrey auction (single unit auction) will be efficient i.e. will put the goods in the hands of the buyers that value them most. However, the conclusion from this paper is that because of overvaluation of bidders the main result is inefficient, i.e. bids are too high. When weak and strong bidders are compared the main conclusion is that strong bidders’ expected payoff is higher in second price auction (SPA), while weak bidder prefers first price auction (FPA) bid.

Revenue Guarantee Equivalence

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders’ values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions are revenue guarantee equivalent: they have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered. (JEL D44, D83)

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. First, we characterize the unique equilibrium outcome in the first price auction for any values of parameters. Then we compare the first price auction with the second price auction in terms of expected revenue. Under the assumption that the probabilities of low values are the same for the two bidders, we obtain two main results: (i) the second price auction yields a higher revenue unless the distribution of a bidder’s valuation first-order stochastically dominates the distribution of the other bidder’s valuation “in a strong sense” and (ii) introducing reserve prices implies that the first price auction is never superior to the second price auction. In addition, in some cases, the revenue in the first price auction decreases when all the valuations increase.