Endogenous budget constraints in auctions

In prior literature, bidders’ budget constraints have been shown to change revenue and efficiency rankings among auction formats. These results, however, are based on the implicit assumption that the nature of the budget constraint is unaffected by auction rules. I extend the standard symmetric model of auctions for a single good to include principals responsible for deciding on the bidder’s budget. Each principal optimally constrains the bidder to mitigate an agency problem between the two. I show that the outcomes of the first and second price auctions generally agree with those from auction models without budget constraints. Bidders likely face budget constraints in many real-world auctions, especially in the sale of valuable assets such as wireless spectrum (Cramton, 1995; Salant, 1997; Bulow et al., 2009), and these constraints potentially have important strategic effects on the outcomes of auction models that cannot be captured in standard frameworks. Current literature on the subject (most notably Che and Gale, 1998) argues that incorporating budget constraints into the standard independent private values model invalidates some well-known results like the revenue equivalence theorem (Riley and Samuelson, 1981; Myerson, 1981). For example, in a model where bidders valuations are private and i.i.d. Che and Gale (1998) show that ∗Department of Economics, University of Maryland, College Park, Address: 3105 Tydings Hall, College Park, MD 20742, USA, telephone: 1-301-405-3528, e-mail: [email protected]. The author is grateful to Lawrence Ausubel, Peter Cramton, Daniel Vincent, Oleg Baranov, Terence Johnson, and Sushant Acharya for advice and suggestions.