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Second‐Price Auctions with Different Participation Costs
Author(s) -
Cao Xiaoyong,
Tian Guoqiang
Publication year - 2013
Publication title -
journal of economics and management strategy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.672
H-Index - 68
eISSN - 1530-9134
pISSN - 1058-6407
DOI - 10.1111/jems.12004
Subject(s) - monotonic function , common value auction , economics , regular polygon , distribution (mathematics) , mathematics , mathematical economics , value (mathematics) , econometrics , cutoff , microeconomics , statistics , mathematical analysis , physics , geometry , quantum mechanics
This paper studies equilibria of second‐price auctions in independent private value environments with different participation costs. Two types of equilibria are identified: monotonic equilibria in which a bidder with a lower participation cost results in a lower cutoff for submitting a bid, and nonmonotonic equilibria in which a lower participation cost results in a higher cutoff. We show that there always exists a monotonic equilibrium, and further, that the monotonic equilibrium is unique for either concave distribution functions or strictly convex distribution functions with nonincreasing reverse hazard rates. There exist nonmonotonic equilibria when the distribution functions are strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limiting properties of equilibria when the difference in bidders’ participation costs approaches zero.