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 study the investment incentives created by truthful mechanisms that allocate resources using approximation algorithms. Some approximation algorithms guarantee nearly 100% of the optimal welfare in the allocation problem but guarantee nothing when accounting for investment incentives. An algorithm's allocative and investment guarantees coincide if and only if its confirming negative externalities are sufficiently small. We introduce fast approximation algorithms for the knapsack problem that have no confirming negative externalities and guarantees close to 100% for both allocation and investment.