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Consider an extensive‐form mechanism, run by an auctioneer who communicates sequentially and privately with bidders. Suppose the auctioneer can deviate from the rules provided that no single bidder detects the deviation. A mechanism is credible if it is incentive‐compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first‐price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy‐proof mechanism.

We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three perspectives: waiting, optimization, and information. The main insight of our analysis is that waiting to thicken the market can be substantially more important than increasing the speed of transactions, and this is quite robust to the presence of waiting costs. From an optimization perspective, naïve local algorithms, that choose the right time to match agents but do not exploit global network structure, can perform very close to optimal algorithms. From an information perspective, algorithms that employ even partial information on agents' departure times perform substantially better than those that lack such information. To elicit agents' departure times, we design an incentive-compatible continuous-time dynamic mechanism without transfers.Keywords: Market Design, Matching, Networks, Continuous-time Markov Chains, Mechanism Design JEL Classification Numbers: D47, C78, C60 * We thank Paul Milgrom and Alvin Roth for valuable comments and suggestions. We also thank Itai Ashlagi, Timothy Bresnahan, Gabriel Carroll, Fuhito Kojima, Matthew Jackson, Muriel Niederle, Afshin Nikzad, Malwina Luczak, Michael Ostrovsky, Bob Wilson, and Alex Wolitzky for their valuable comments, as well as several seminar participants for helpful suggestions. All errors remain our own.

and to Alexei Pozdnukhov at Replica for the ongoing cooperation. Alex Weinberg provided outstanding research assistance throughout this project. We also thank Stephen Eubank and the University of Virginia Biocomplexity Institute, Tim Bresnahan, Matt Jackson, and Mike Whinston for their insightful comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. At least one co-author has disclosed a financial relationship of potential relevance for this research. Further information is available online at http://www.nber.org/papers/w27374.ack NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

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