Auctions with Contingent Payments

Abstract

There now exists a host of results concerning the revenue performance of various auction methods. This note delves deeper into auction markets by examining the effects on sellers' revenue of certain noncash means of payment. The basic result-that bidding mediums which include some contingent pricing feature generally yield the seller more revenue than do cash bids-is intriguing by itself and also points out the limitations of received theory. Since what follows builds on the independent-preferences framework, it is useful to first note the assumptions of that model and the major results pertaining to it. To model an auction in the independent-preferences tradition, one assumes that bidders have reservation values, Vi, that are known only privately and that can be depicted as being drawn independently from some distribution F( V). The most important result for this model is the revenue equivalence theorem: as given in John Riley and William Samuelson (1981), any auction involving risk-neutral bidders for which the following four conditions hold: (a) a buyer can make any bid above some minimum reserve price, (b) the buyer making the highest bid is awarded the object, (c) the auction rules are anonymous, and (d) there is a common equilibrium bidding strategy in which each buyer makes a bid bi, which is a strictly increasing function of his reservation value Vi, yields an expected revenue of

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