Abstract
In a classical result, Milgrom (1981a) established that the Monotone Likelihood Ratio Property (MLRP) is a sufficient condition for the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions. We show: (1) If MLRP is violated, then for any number of bidders and objects there exists a distribution of the common value such that no increasing symmetric equilibrium exists; (2) If MLRP is violated, then for any distribution of the common value there exist infinitely many pairs of the number of bidders and the number of objects such that an increasing symmetric equilibrium does not exist; (3) There are examples where an increasing symmetric equilibrium exists even when the signal distribution violates MLRP.
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References
Athey S (2001) Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica 69: 861–890
David H, Nagaraja H (2003) Order statistics, 3rd edn. Wiley, New York
Jackson M (2005) Non-existence of equilibrium in Vickrey, second-price, and English auctions. California Institute of Technology, Mimeo
Jackson M, Swinkels J (2005) Existence of equilibrium in single and double private value auctions. Econometrica 73: 93–139
Klemperer P (1999) Auction theory: a guide to the literature. J Econ Surveys 13: 227–286
Levin D, Smith JL (1991) Some evidence on the winner’s curse: Comment. Am Econ Rev 81: 370–375
Maskin E, Riley J (2000) Equilibrium in sealed high bid auctions. Rev Econ Stud 67: 439–452
Milgrom PR (1981a) Rational expectations, information acquisition, and competitive bidding. Econometrica 49: 921–943
Milgrom PR (1981b) Good news and bad news: representation theorems and applications. Bell J Econ 12: 380–391
Milgrom PR, Weber RJ (1982) A theory of auctions and competitive bidding. Econometrica 50: 1089–1122
Pesendorfer W, Swinkels JM (1997) The loser’s curse and information aggregation in common value auctions. Econometrica 65: 1247–1281
Topkis DM (1978) Minimizing a submodular function on a lattice. Oper Res 26: 305–321
Winkler RL, Brooks DG (1980) Competitive bidding with dependent value estimates. Oper Res 28: 603–613
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Tsetlin, I., Pekeč, A.S. On the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions. Rev. Econ. Design 10, 63–71 (2006). https://doi.org/10.1007/s10058-006-0005-0
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DOI: https://doi.org/10.1007/s10058-006-0005-0