Description:
We study mediated many-to-many matching in markets in which valuations evolve over time as the result of shocks, learning through experimentation, or a preference for variety. The analysis uncovers the key tradeoffs that platforms face in the design of their matching protocols. It shows that the dynamics that maximize either the platform's profits or welfare can often be sustained through auctions implementing the matches with the highest bilateral score up to capacity. In equilibrium, bidding is straight-forward and myopic. The analysis also sheds light on the merits of regulating such markets. When match values are positive, profit maximization involves fewer and shorter interactions than welfare maximization. This conclusion need not extend to markets where certain agents dislike certain interactions.