Two-Bidder All-Pay Auctions with Interdependent Valuations, Including the Highly Competitive Case

41 Pages Posted: 7 Jun 2014 Last revised: 25 Nov 2015

See all articles by Lucas Rentschler

Lucas Rentschler

Utah State University - Department of Economics and Finance

Theodore Turocy

University of East Anglia (UEA)

Date Written: November 24, 2015

Abstract

We analyze symmetric, two-bidder all-pay auctions with interdependent valuations and discrete type spaces. Relaxing previous restrictions on the distribution of types and the valuation structure, we present a construction that characterizes all symmetric equilibria. We show how the search problem this construction faces can be complex. In equilibrium, randomization can take place over disjoint intervals of bids, equilibrium supports can have a rich structure, and non-monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common. Particular attention is paid to the case in which an increase in a bidder’s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are “highly competitive” in the sense that the bidder’s higher valuation also signals that the other bidder has an incentive to bid aggressively.

Keywords: contests, all-pay auctions, mixed strategies

JEL Classification: D44, D82, D72

Suggested Citation

Rentschler, Lucas and Turocy, Theodore, Two-Bidder All-Pay Auctions with Interdependent Valuations, Including the Highly Competitive Case (November 24, 2015). Available at SSRN: https://ssrn.com/abstract=2446789 or http://dx.doi.org/10.2139/ssrn.2446789

Lucas Rentschler

Utah State University - Department of Economics and Finance ( email )

Logan, UT 84322-1400
United States

Theodore Turocy (Contact Author)

University of East Anglia (UEA) ( email )

Norwich Research Park
Norwich, Norfolk NR4 7TJ
United Kingdom

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