Matching auctions

This paper is about (platform) mediated matching in markets in which valuations evolve over time. We introduce and then study a class of dynamic matching auctions where, in each period, agents from two sides of a market submit multiple bids, one for each possible partner. Each match receives a “score” that is a weighted average of the involved agents’ reciprocal bids, net of the platform’s match-specific costs. The weights are determined by the agents’ membership statuses and vary with the platform’s objectives. In each period, the matches that maximize the sum of the bilateral scores subject to individual and aggregate capacity constraints are implemented. We show that, under appropriate conditions, this class includes both welfareand profit-maximizing mechanisms. When match values are positive and none of the capacity constraints binds, profit maximization results in fewer interactions than welfare maximization, in each period. This conclusion need not extend to markets in which individual and/or aggregate capacity constraints bind and/or agents dislike certain interactions. Finally, we discuss how similar auctions but with forward-looking “index scores” can be used in markets where match values depend on past interactions, for example due to experimentation, a preference for variety, or habit formation. JEL Classification Numbers: D82, C73, L1.