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Asymmetric Budget Constraints in a First Price Auction

Nina Bobkova ()

MPRA Paper from University Library of Munich, Germany

Abstract: I solve a first-price auction for two bidders with asymmetric budget distributions and known valuations for one object. I show that in any equilibrium, the expected utilities and bid distributions of both bidders are unique. If budgets are sufficiently low, the bidders will bid their entire budget in any equilibrium. For sufficiently high budgets, mass points in the equilibrium strategies arise. A less restrictive budget distribution could make both bidders strictly worse off. If the budget distribution of a bidder is dominated by the budget distribution of his opponent in the reverse-hazard rate order, the weaker bidder will bid more aggressively than his stronger opponent. In contrast to existing results for symmetric budget distributions, with asymmetric budget distributions, a second-price auction can yield a strictly higher revenue than a first-price auction. Under an additional assumption, I derive the unique equilibrium utilities and bid distributions of both bidders in an all-pay auction.

Keywords: Budget Constraints; First Price Auctions; Asymmetric Bidders (search for similar items in EconPapers)
JEL-codes: C72 D44 D82 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-upt
Date: 2017-02-03, Revised 2018-08
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