This paper presents conditions under which a person's beliefs about the occurrence of uncertain events are quantified by a capacity measure, i.e., a nonadditive probability. Additivity of probability is violated in a large number of applications where probabilities are vague or ambiguous due to lack of information.The key feature of the theory presented in this paper is a separation of the derivation of capacities for events from a specific choice model. This is akin to eliciting a probability distribution for a random variable without committing to a specific decision model. Conditions are given under which Choquet expected utility, the Machina-Schmeidler probabilistically sophisticated model, and subjective expected utility can be derived as special cases of our general model.

This paper provides an extension of Savage's subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive as well as ambiguous events for which probabilities are permitted to be nonadditive. The main axiom is cumulative dominance which adapts stochastic dominance to decision making under uncertainty. We derive a Choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation. The relationship of our approach with that of Schmeidler who uses a two-stage formulation to derive Choquet expected utility is also explored.

The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a "nearby" instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two.

An obstacle to using market mechanisms to allocate indivisible goods is the lack of competitive equilibria (CEs). Arrow and Hahn introduced social-approximate equilibria: price vectors with “small” excess demands. We define preferences called Δ-substitutes, where social-approximate equilibria exist with good-by-good excess demand bounded by 2(Δ−1), independent of economy size. For Δ=1, CEs exist even with income effects. A Δ greater than 1 allows for richer substitutability and complementarity patterns, broadening the scope for market mechanisms to allocate indivisible goods.

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. We give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent.

Abstract We present results from a large-scale randomized experiment across 350 schools in Tanzania that studied the impact of providing schools with (i) unconditional grants, (ii) teacher incentives based on student performance, and (iii) both of the above. After two years, we find (i) no impact on student test scores from providing school grants, (ii) some evidence of positive effects from teacher incentives, and (iii) significant positive effects from providing both programs. Most important, we find strong evidence of complementarities between the programs, with the effect of joint provision being significantly greater than the sum of the individual effects. Our results suggest that combining spending on school inputs (the default policy) with improved teacher incentives could substantially increase the cost-effectiveness of public spending on education.