Ranking equilibrium competition in auctions with participation costs

•We study the degrees of equilibrium competition in three common forms of auctions with costly participation.•We show that, when the valuation distribution is concave, there is a simple condition to rank the equilibrium competition in those auctions.•We also investigate the relationship between stochastic order and the degree of equilibrium competition in those auctions.

This paper studies the degrees of equilibrium competition in three common forms of auctions with costly participation, and shows that, when bidders' valuation distribution is concave, there is a simple condition to rank the equilibrium competition of those auctions. It also investigates how the results are related to stochastic ordering of bidders' valuation distributions, and provides some illustrative examples.