Intuitive and noncompetitive equilibria in weakly efficient auctions with entry costs

I study weakly efficient auctions with entry costs, under the IPV assumption, following Tan and Yilankaya [Tan, G., Yilankaya, O., 2006. Equilibria in second price auctions with participation costs. Journal of Economic Theory 130, 205–219]. First, I generalize their Proposition 4 to what I call (generalized) intuitive equilibrium. By such I prove that if bidders’ valuation distributions are ordered in a (weak) first order domination ranking, then there exists an equilibrium in cutoff strategies where cutoffs are (weakly) increasingly ordered with respect to the domination ranking. Stronger bidders are thus ex ante more likely to participate. A second result states a necessary and sufficient condition for the existence of a noncompetitive cutoff equilibrium, in which only one bidder (if any) takes part in the auction. Neither the uniform distribution nor any distribution first order stochastically dominated by the uniform may ever satisfy that condition. If both intuitive and nonintuitive equilibria exist, I conjecture that intuitive equilibria tend to yield higher ex ante efficiency, while nonintuitive ones might yield higher expected revenues.