Theories on Auctions with Participation Costs

Abstract

In this dissertation I study theories on auctions with participation costs with various information structure. Chapter II studies equilibria of second price auctions with differentiated participation costs. We consider equilibria in independent private values environments where bidders? entry costs are common knowledge while valuations are private information. We identify two types of equilibria: monotonic equilibria in which a higher participation cost results in a higher cutoff point for submitting a bid, and neg-monotonic equilibria in which a higher participation cost results in a lower cutoff point. We show that there always exists a monotonic equilibrium, and further, that the equilibrium is unique for concave distribution functions and strictly convex distribution functions with some additional conditions. There exists a neg-monotonic equilibrium when the distribution function is strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limit status of equilibria when the difference in bidders' participation costs approaches zero. Chapter III studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogenous. Moreover, we identify a sufficient condition under which we have a unique equilibrium in a heterogeneous economy with two bidders. Our general framework covers many relevant models in the literature as special cases. Chapter IV characterizes equilibria of first price auctions with participation costs in the independent private values environment. We focus on the cutoff strategies in which each bidder participates and submits a bid if his value is greater than or equal to a critical value. It is shown that, when bidders are homogenous, there always exists a unique symmetric equilibrium, and further, there is no other equilibrium when valuation distribution functions are concave. However, when distribution functions are elastic at the symmetric equilibrium, there exists an asymmetric equilibrium. We find similar results when bidders are heterogenous.