All-pay auctions with ties

Alan Gelder (), Dan Kovenock and Brian Roberson ()
Additional contact information
Alan Gelder: Institute for Defense Analyses
Brian Roberson: Purdue University

Economic Theory, 2022, vol. 74, issue 4, No 8, 1183-1231

Abstract: Abstract We study the two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Players thus engage in two margins of competition: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory and the value of tying relative to winning. We fully characterize the set of Nash equilibria for the entire parameter space. For much of the parameter space, there is a unique Nash equilibrium which is also symmetric. Equilibria typically involve randomizing over multiple disjoint intervals, so that in essence players randomize between attempting to tie and attempting to win. In equilibrium, expected bids and payoffs are non-monotonic in both the margin required for victory and the relative value of tying.

Keywords: All-pay auction; Contest; Ties; Draws; Bid differential (search for similar items in EconPapers)
JEL-codes: C72 D44 D72 D74 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Working Paper: All-Pay Auctions with Ties (2016)
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DOI: 10.1007/s00199-019-01195-7

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