Multi-unit auctions with budget-constrained bidders

In my dissertation, I investigate the effects of budget-constraints in multi-unit auctions. This is done in three parts. First, I analyze a case where all bidders have a common budget constraint. Precisely, I analyze an auction where two units of an object are sold at two simultaneous, sealed bid, first-price auctions, to bidders who have demand for both units. Bidders differ with respect to their valuations for the units. All bidders have an identical budget constraint which binds their ability to spend in the auction. I show that if valuation distribution is atom-less, then their does not exist any symmetric equilibrium in this auction game.

In the second and third parts of my thesis, I analyze the sale of licenses for the right to drill for oil and natural gas in the Outer Continental Shelf (OCS) of the United States. These sales are conducted using simultaneous sealed-bid first-price auctions for multiple licenses, each representing a specific area (called a tract). Using aspects of observed bidding-behavior, I first make a prima facie case that bidders are budget-constrained in these auctions. In order to formalize this argument, I develop a simple extension of the standard model (where bidders differ in their valuations for the objects) by incorporating (random) budgets for the bidders. The auction-game then has a two-dimensional set of types for each player. I study the theoretical properties of this auction, assuming for simplicity that two units are being sold. I show that this game has an equilibrium in pure strategies that is symmetric with respect to the players and with respect to the units. The strategies are essentially pure in the sense that each bidder-type has a unique split (up to a permutation) of his budget between the two auctions. I then characterize the equilibrium in terms of the bid-distribution and iso-bid curves in the value-budget space. I derive various qualitative features of this equilibrium, among which are: (1) under mild assumptions, there always exist bidder-types who submit unequal bids in equilibrium, (2) the equilibrium is monotonic in the sense that bidders with higher valuations prefer more unequal splits of their budgets than bidders with lower valuations and the same budget-level.

With a formal theory in place, I carry out a quantitative exercise, using data from the 1970 OCS auction. I show that the model is able to match many aspects of the data. (1) In the data, the number of tracts bidders submit bids on is positively correlated with budgets (an R² of 0.84), even though this relationship is non-monotonic; my model is able to capture this non-monotonicity, while producing an R² of 0.89 (2) In the data, the average number of bids per tract is 8.21; for the model, this number is 10.09. (3) Auction revenue in the data was $1.927 billion; the model produced a mean revenue of $1.944 billion