This paper proposes a new mechanism for combinatorial assignment—for example, assigning schedules of courses to students—based on an approximation to competitive equilibrium from equal incomes (CEEI) in which incomes are unequal but arbitrarily close together. The main technical result is an existence theorem for approximate CEEI. The mechanism is approximately efficient, satisfies two new criteria of outcome fairness, and is strategyproof in large markets. Its performance is explored on real data, and it is compared to alternatives from theory and practice: all other known mechanisms are either unfair ex post or manipulable even in large markets, and most are both manipulable and unfair.

We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategy-proofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism’s “prices” as exogenous to her report—be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism—has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (1) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (2) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate SP, which evaluates incentives to manipulate ex post and as a result is too strong to obtain our main results in support of SP-L, and the traditional notion of approximate Bayes-Nash incentive compatibility, which, like SP-L, evaluates incentives to manipulate ex interim, but which imposes common knowledge and strategic sophistication assumptions that are often viewed as unrealistic.

Our recent research (Budish, Cramton, and Shim 2013) proposes frequent batch auctions - uniform-price sealed-bid double auctions conducted at frequent but discrete time intervals - as a market design alternative to continuous-time trading in financial markets. This short paper discusses the implementation details of frequent batch auctions. We outline the process flow for frequent batch auctions, discuss a modification to the market design that accommodates market fragmentation and Reg NMS, and discuss the engineering and economic considerations relevant for determining the batch interval. Open questions are discussed throughout.

A well-developed theoretical literature - dating back at least to Nordhaus (1969) - has analyzed optimal patent policy design. We re-present the core trade-off of the Nordhaus model and highlight an empirical question which emerges from the Nordhaus framework as a key input into optimal patent policy design: namely, what is the elasticity of R&D investment with respect to the patent term? We then review the - surprisingly small - body of empirical evidence that has been developed on this question over the nearly half century since the publication of Nordhaus's book.

Randomization is commonplace in everyday resource allocation. We generalize the theory of randomized assignment to accommodate multi-unit allocations and various real-world constraints, such as group-specific quotas (“controlled choice”) in school choice and house allocation, and scheduling and curriculum constraints in course allocation. We develop new mechanisms that are ex ante efficient and fair in these environments, and that incorporate certain non-additive substitutable preferences. We also develop a “utility guarantee” technique that limits ex post unfairness in random allocations, supplementing the ex ante fairness promoted by randomization. This can be applied to multi-unit assignment problems and certain two-sided matching problems.