Characterizing Truthful Market Design

This paper characterizes the family of truthful double-sided auctions. Despite the importance of double-sidedauctions to market design, to date no characterizationof truthful double-sided auctions was made. This pa-per characterizes truthful mechanisms for double-sidedauctions by generalizing Roberts classic result [29], toshow that truthful double-sided auctions must ”almost”be affine maximizers.Our main result of characterizing double-sided auc-tions required the creation of a new set of tools, reduc-tions that preserve economic properties. This paperutilizes two such reductions; a truth-preserving reduc-tion and a non-affine preserving reduction. The truth-preserving reduction is used to reduce the double-sidedauction to a special case of a combinatorial auction tomake use of the impossibility result proved in [20]. Intu-itively, our proof shows that truthful double-sided auc-tions are as hard to design as truthful combinatorialauctions.Two important concepts are developed in additionto the main result. First, the form of reduction usedin this paper is of independent interest as it providesa means for comparing mechanism design problems bydesign difficulty. Second, we define the notion of ex-tension of payments; which given a set of payments forsome players finds payments for the remaining play-ers. The extension payments maintain the truthful andaffine maximization properties.