We introduce two linear pricing mechanisms for quasilinear economies in which market-clearing prices may not exist. Electricity markets, fisheries markets, and many others include producers with start-up costs, ramping costs, or other fixed costs that fail the convexity assumptions traditionally used to prove that clearing prices exist.

In many real-world resource allocation problems, optimization is computationally intractable, so any practical allocation mechanism must be based on an approximation algorithm. We study investment incentives in strategy-proof mechanisms that use such approximations. In sharp contrast with the Vickrey-Clark-Groves mechanism, for which individual returns on investments are aligned with social welfare, we find that some algorithms that approximate efficient allocation arbitrarily well can nevertheless create misaligned investment incentives that lead to arbitrarily bad overall outcomes. However, if a near-efficient algorithm "excludes bossy negative externalities," then its outcomes remain near-efficient even after accounting for investments. A weakening of this "XBONE" condition is necessary and sufficient for the result.

Over 13 months in 2016-17 the US Federal Communications Commission (FCC) conducted an "incentive auction" to repurpose radio spectrum from broadcast television to wireless internet. The result of the auction was to remove 14 UHF-TV channels from broadcast use, sell 70 MHz of wireless internet licenses for $19.8 billion, and create 14 MHz of spectrum for unlicensed uses. With fewer UHF channels remaining for TV broadcast, the TV spectrum was also reorganized. Each station was either "repacked" in the leftover channels or voluntarily sold its broadcast rights, either going off the air or switching to a different band. The volunteers received a total of $10.05 billion to yield or exchange their rights and make repacking possible.

We model an online display advertising environment with brand advertisers and better-informed performance advertisers, and seek an auction mechanism that is strategy-proof, anonymous and insulates brand advertisers from adverse selection. We find that the only such mechanism that is also false-name proof assigns the item to the highest bidding performance advertiser only when the ratio of the highest bid to the second highest bid is sufficiently large. For fat-tailed match-value distributions, this new mechanism captures most of the gains from good matching and improves match values substantially compared to the common practice of setting aside impressions in advance.

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We propose two different methods for presenting substitutes (a.k.a. gross-substitutes) valuations. Each provides short descriptions for a family of substitutes valuations. We also show that substitutes valuation are closed under k-satiation.