Pure Strategy Equilibria in Auctions under more General Assumptions
Luciano I de Castro
auctions | pure strategy equilibria | tie-breaking rule | Affiliation
This thesis deals with Pure Strategy Equilibria in Auctions. We begin by introducing the subject through a presentation of its fundamentals and a survey of the main results. After a basic result about the bidding behavior, we study auctions with multidimensional types and without monotonic assumptions. We are able to give new existence results for this kind of symmetric auctions, with independent types. We also show that a simple tie-breaking rule is sufficient to ensure the existence of pure strategy equilibrium. We apply these results to the study of single object auctions with multidimensional bids. We also give a new proof of equilibrium existence for monotonic asymmetric auctions, in a setting that includes new results, e.g., the pure strategy equilibrium existence for asymmetric double auctions. All these results are under the assumption of independence. We argue that affiliation, the assumption normally used as a generalization of independence, is not convenient. Finally, we present a fixed point theorem for set-valued maps that does not need the assumption of convex values.