First-Price Auctions with Budget Constraints

Consider a first-price sealed-bid auction where participants have affiliated valuations and private budget constraints; that is, bidders have private multidimensional types. This article investigates the existence and nature of monotone equilibria in this setting. Hard budget constraints introduce two competing effects on bidding. The direct effect depresses bids as participants hit their spending limit. The strategic effect encourages more aggressive bidding by participants with large budgets. Together these effects can yield discontinuous equilibrium strategies stratifying competition along the budget dimension. The strategic consequences of private budget constraints can be a serious confound in interpreting bidding behavior in auctions.