Monotonicity and rationalizability in a large first price auction

In Koo Cho

Research output: Contribution to journalArticle

Abstract

This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases (Wilson, 1977). Instead of analysing the symmetric Nash equilibrium, we examine rationalizable strategies (Bernheim (1984), Pearce (1984)) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the "truthful" valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to that of Wilson (1977), while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed.

Original languageEnglish (US)
Pages (from-to)1031-1055
Number of pages25
JournalReview of Economic Studies
Volume72
Issue number4
DOIs
StatePublished - Oct 1 2005

ASJC Scopus subject areas

  • Economics and Econometrics

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