Econometrics of Sealed-bid Auctions

1. Introduction. Recent empirical and anecdotal evidence suggests that different auction rules generate important differences in bidding behavior. Milgrom (1996) compares auctions for the sale of the radio spectrum held in the United States, New Zealand and Australia. The Australian and New Zealand auctions were characterized by wildly different prices for similar bandwidths. In the United States price differences between identical bandwidths were of a far smaller magnitude. Milgrom argues that the different rules of the auctions can account for the different bidding behavior in the United States, Australia, and New Zealand. Kagel (1995) surveys a wealth of experimental evidence that documents how different auction rules change subjects' bidding behavior. Applied work in auctions clearly needs to take account of the " rules of the game ". Game theoretic models of auctions allow the economist to clearly specify the strategies and utility functions of the bidders. There now exists a large body of economic theory that studies the equilbria to a wide variety of auction games. (See Wilson (1992) and McAfee and McMillan (1987) for surveys.) The standard auction models assume that the players do not know each other's valuations for the good being auctioned. The standard solution concept of Bayes-Nash equilibrium, if it exists, generates a distribution of observed bids resulting from every agent in the game maximizing utility. The equilibrium distribution of bids can be used as a likelihood function for applied work in economics. In particular, if the likelihood function can be evaluated efficiently, Markov chain Monte Carlo can be used to simulate the posterior distribution of model parameters. (See Geweke (1994) and Tierney (1994) for overviews of these methods.) The posterior distribution of model parameters allows the econometrician to use observed bids to learn about the economic primitives, such as the utility functions and the information structure that generated the bids. Paarsch (1992) and Laffont, Ossard, and Vuong (1995) discuss estimation procedures applicable in first price sealed bid auctions, that is, auctions where all bidders submit sealed bids and the highest bidder wins the auction. The authors make a number of assumptions about the game to render their econometric problem tractable: all bidders are ex-ante identical, it is costless