Second-Price Auctions with Different Participation Costs


  • We thank Shengyu Li, Xianwen Shi, Guofu Tan, Mingjun Xiao, and Okan Yilankaya as well as two anonymous referees for helpful comments and discussions. Xiaoyong Cao thanks the financial support from National Natural Science Foundation of China (NSFC-71201030). Financial support from the National Natural Science Foundation of China (NSFC-70773073), 211 Leading Academic Discipline Program for Shanghai University of Finance and Economics (the third phase), and the Program to Enhance Scholarly Creative Activities at Texas A&M University is gratefully acknowledged by Guoqiang Tian.


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.