Eco514-Game Theory Lecture 8: Applications(1)-Simultaneous Auctions Marciano siniscalchi October 12. 1999 Introduction This lecture, as well as the next, exemplify applications of the framework and techniques developed so far to problems of economic interest. Neither lecture attempts to cover the example applications in any generality, of course; you may however find these topics of sufficient interest to warrant further study Auction theory is generally indicated as one of the "success stories"of game theory There is no doubt that the game-theoretic analysis of auctions has informed design decisions of great practical relevance. If you are interested in recent applications of auction theory, youshoulddefinitelycheckoutthefollowingUrl:http://www.market-design.comin particular, the Library section contains downloadable working papers in PDF format) This lecture focuses on the simplest possible setting, in which a single good is offered for sale, and bidders are required to submit their offers in a sealed envelope (so we are ruling out ascending or descending auctions: but see below ) Also, I shall focus on the analysis of"popular"auction forms: Myerson's 1981 paper deals with optimal auctions from a mechanism design standpoint. Finally, I will employ equilibrium analysis throughout Framework and auction forms The basic bidding game form may be represented as follows: each bidder i E N submit a bid ai E Ai=R+(so we rule out negative bids ); given any bid profile a =(aiieN, the auctioneer determines the set of high bidders H(a) according to H(a)={i∈N:≠,a1≥a Finally, the object is randomly assigned to one of the high bidders(each of whom equally likely to receive it), referred to as the winning bidder. Thus, the winning bidder is a high bidder, but only one high bidder will be the winning bidder.Eco514—Game Theory Lecture 8: Applications (1)—Simultaneous Auctions Marciano Siniscalchi October 12, 1999 Introduction This lecture, as well as the next, exemplify applications of the framework and techniques developed so far to problems of economic interest. Neither lecture attempts to cover the example applications in any generality, of course; you may however find these topics of sufficient interest to warrant further study. Auction theory is generally indicated as one of the “success stories” of game theory. There is no doubt that the game-theoretic analysis of auctions has informed design decisions of great practical relevance. If you are interested in recent applications of auction theory, you should definitely check out the following URL: http://www.market-design.com (in particular, the Library section contains downloadable working papers in PDF format). This lecture focuses on the simplest possible setting, in which a single good is offered for sale, and bidders are required to submit their offers in a sealed envelope (so we are ruling out ascending or descending auctions: but see below). Also, I shall focus on the analysis of “popular” auction forms: Myerson’s 1981 paper deals with optimal auctions from a mechanism design standpoint. Finally, I will employ equilibrium analysis throughout. Framework and Auction Forms The basic bidding game form may be represented as follows: each bidder i ∈ N submits a bid ai ∈ Ai = R+ (so we rule out negative bids); given any bid profile a = (ai)i∈N , the auctioneer determines the set of high bidders H(a) according to H(a) = {i ∈ N : ∀j 6= i, ai ≥ aj}. Finally, the object is randomly assigned to one of the high bidders (each of whom is equally likely to receive it), referred to as the winning bidder. Thus, the winning bidder is a high bidder, but only one high bidder will be the winning bidder.1 1