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In Kenneth Arrow’s last week of life at age 95, he reported that “I began my research career with an impossibility theorem. If I had time now, my last theorem would be an impossibility theorem about social choice for environmental policy.” This paper completes the formalization, proof, and discussion of the theorem that Arrow then described. 

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 itsconfirming negative externalitiesare 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. 

A common pattern of control in firms is for management to retain a broad set of rights, whereas the remaining stakeholders’ contracts provide them with targeted veto rights over specific classes of decisions. We explain this pattern of control sharing as an efficient organizational response that balances the need to encourage management to account for stakeholders’ interests against the need to prevent self-interested stakeholders from blocking valuable proposals. Enforceable obligations of good faith and fair dealing play an essential role in facilitating undivided management control of many decisions. With these legal protections (but not without them), shared control is more likely when the parties are more symmetrically informed and hence, better able to bargain to efficient decisions. This paper was accepted by Joshua Gans, business strategy. 

Combinatorial auctions have found widespread application for allocating multiple items in the presence of complex bidder preferences. The enumerative exclusive OR (XOR) bid language is the de facto standard bid language for spectrum auctions and other applications, despite the difficulties, in larger auctions, of enumerating all the relevant packages or solving the resulting NP-hard winner determination problem. We introduce the flexible use and efficient licensing (FUEL) bid language, which was proposed for radio spectrum auctions to ease both communications and computations compared with XOR-based auctions. We model the resulting allocation problem as an integer program, discuss computational complexity, and conduct an extensive set of computational experiments, showing that the winner determination problem of the FUEL bid language can be solved reliably for large realistic-sized problem instances in less than half an hour on average. In contrast, auctions with an XOR bid language quickly become intractable even for much smaller problem sizes. We compare a sealed-bid FUEL auction to a sealed-bid auction with an XOR bid language and to a simultaneous clock auction. The sealed-bid auction with an XOR bid language incurs significant welfare losses because of the missing bids problem and computational hardness, the simultaneous clock auction leads to a substantially lower efficiency than FUEL because of the exposure problem. This paper was accepted by Axel Ockenfels.