TY - JOUR

T1 - Monotonicity and rationalizability in a large first price auction

AU - Cho, In Koo

N1 - Funding Information:
Acknowledgements. I am grateful for helpful conversations with Pierpaolo Battigalli, Preston McAfee and Steven Williams, and insightful criticisms from two anonymous referees and the editor, Mark Armstrong. Financial support from the National Science Foundation (SES-0004315) is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

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U2 - 10.1111/0034-6527.00360

DO - 10.1111/0034-6527.00360

M3 - Article

AN - SCOPUS:27744462872

SN - 0034-6527

VL - 72

SP - 1031

EP - 1055

JO - Review of Economic Studies

JF - Review of Economic Studies

IS - 4

ER -