Non-monotoniticies and the all-pay auction tie-breaking rule
type: Item
instance of: scholarly article
title: Non-monotoniticies and the all-pay auction tie-breaking rule
zbMATH Open document ID: 1159.91012
author: Luciano I. de Castro
author: Humberto Moreira
author: Aloisio Araujo
published in: Economic Theory
publication date: 2008-05-26T00:00:00Z
review text: Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The fact that the equilibrium existence for discontinuous games depends on special definition of the payoff at discontinuities was first pointed out for games of complete information by \textit{L. K. Simon} and \textit{W. R. Zame} [Econometrica 58, No. 4, 861--872 (1990; Zbl 0729.90098)], and for games of incomplete information by \textit{M. O. Jackson, L. K. Simon, J. M. Swinkels} and \textit{W. R. Zame} [Econometrica 70, No. 5, 1711--1740 (2002), corrigendum 72, No. 6, 1927--1929 (2004; Zbl 1106.91348)]. Next, \textit{A. Araujo} and \textit{L. I. de Castro} [Games Econ. Behav. 65, No. 1, 25--48 (2009; Zbl 1165.91373)] proved equilibrium existence for single and double asymmetric auctions with interdependent values. The present paper characterizes when a special tie-breaking rules are really needed. The result is established for the set of symmetric auctions with unidimensional types, and partially for a set of multidimensional symmetric auctions with weak monotonicity assumptions. When a special tie-breaking rule is needed, the authors show that the all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information.
reviewed by: Małgorzata Doman
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91B44
zbMATH DE Number: 5278998
zbMATH Keywords: discontinuous game
zbMATH Keywords: auction
zbMATH Keywords: all-pay auction
zbMATH Keywords: tie-breaking rule
zbMATH Keywords: pure strategy equilibrium
zbMATH Keywords: non-monotonic bidding function
MaRDI profile type: Publication
full work available at URL: s00199-007-0249-0
OpenAlex ID: W1552203786
cites work: Pure strategy equilibria of single and double auctions with interdependent values
cites work: Adverse selection problems without the Spence-Mirrlees condition
cites work: Second-price common-value auctions under multidimensional uncertainty
cites work: Efficient Auctions
cites work: Communication and Equilibrium in Discontinuous Games of Incomplete Information
cites work: Q2774021
cites work: Q3262608
cites work: Optimal Auctions with Risk Averse Buyers
cites work: Equilibrium in Sealed High Bid Auctions
cites work: Formulation of Bayesian analysis for games with incomplete information
cites work: A Theory of Auctions and Competitive Bidding
cites work: Q5475041
cites work: Discontinuous Games and Endogenous Sharing Rules
cites work: High bids and broke winners
DOI: 10.1007/S00199-007-0249-0
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description: scientific article; zbMATH DE number 5278998