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 model of dynamic matching in networked markets, where agents arrive and depart stochastically and the composition of the trade network depends endogenously on the matching algorithm. If the planner can identify agents who are about to depart, then waiting to thicken the market substantially reduces the fraction of unmatched agents. If not, then matching agents greedily is close to optimal. We specify conditions under which local algorithms that choose the right time to match agents, but do not exploit the global network structure, are close to optimal. Finally, we consider a setting where agents have private information about their departure times and design a mechanism to elicit this information.