Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high‐dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non‐inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.

A receiver wants to learn multidimensional information from a sender, and she has the capacity to verify just one dimension. The sender's payoff depends on the belief he induces, via an exogenously given monotone function. We show that by using a randomized verification strategy, the receiver can learn the sender's information fully in many cases. We characterize exactly when it is possible to do so. In particular, when the exogenous payoff function is submodular, we can explicitly describe a full‐learning mechanism; when it is (strictly) supermodular, full learning is not possible. In leading cases where full learning is possible, it can be attained using an indirect mechanism in which the sender chooses the probability of verifying each dimension.

We develop a framework to study the dynamics of vote trading over multiple binary issues. We prove that there always exists a stable allocation of votes that is reachable in a finite number of trades, for any number of voters and issues, any separable preference profile, and any restrictions on the coalitions that may form. If at every step all blocking trades are chosen with positive probability, convergence to a stable allocation occurs in finite time with probability 1. If coalitions are unrestricted, the outcome of vote trading must be Pareto optimal, but unless there are three voters or two issues, it need not correspond to the Condorcet winner.

Private information is at the heart of many economic activities. For decades, economists have assumed that individuals are willing to misreport private information if this maximizes their material payoff. We combine data from 90 experimental studies in economics, psychology, and sociology, and show that, in fact, people lie surprisingly little. We then formalize a wide range of potential explanations for the observed behavior, identify testable predictions that can distinguish between the models, and conduct new experiments to do so. Our empirical evidence suggests that a preference for being seen as honest and a preference for being honest are the main motivations for truth‐telling.

We propose a new solution for discrete exchange economies and resource‐allocation problems, the exclusion core. The exclusion core rests upon a foundational idea in the legal understanding of property, the right to exclude others. By reinterpreting endowments as a distribution of exclusion rights, rather than as bundles of goods, our analysis extends to economies with qualified property rights, joint ownership, and social hierarchies. The exclusion core is characterized by a generalized top trading cycle algorithm in a large class of economies, including those featuring private, public, and mixed ownership. It is neither weaker nor stronger than the strong core.

We study stability of two-sided many-to-one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finite market, we show that a stable matching exists in a large market with a continuum of workers, provided that each firm's choice is convex and changes continuously as the set of available workers changes. We also study the existence and structure of stable matchings under preferences exhibiting substitutability and indifferences in a large market. Building on these results, we show that an approximately stable matching exists in large finite economies. We extend our framework to ensure a stable matching with desirable incentive and fairness properties in the presence of indifferences in firms' preferences.

We study economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to Pareto inefficient allocations; the equilibria coincide with Arrow-Debreu equilibria only if the values of net trades are ambiguity-free in the mean. In economies without aggregate uncertainty, inefficiencies are generic. We introduce a constrained efficiency concept, uncertainty-neutral efficiency, equilibrium allocations under price uncertainty are efficient in this constrained sense. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. Our characterization spans several known solution concepts, including the special cases of the Nash, egalitarian, and utilitarian solutions. Using a probability‐based language, we offer a natural interpretation for the product operator underlying the Nash solution: when the bargainers' individual acceptance probabilities are independent, their product recovers the joint acceptance probability.