The deferred acceptance algorithm is often used to allocate indivisible objects when monetary transfers are not allowed. We provide two characterizations of agent-proposing deferred acceptance allocation rules. Two new axioms, individually rational monotonicity and weak Maskin monotonicity, are essential to our analysis. An allocation rule is the agent-proposing deferred acceptance rule for some acceptant substitutable priority if and only if it satisfies non-wastefulness and individually rational monotonicity. An alternative characterization is in terms of non-wastefulness, population monotonicity and weak Maskin monotonicity. We also offer an axiomatization of the deferred acceptance rule generated by an exogenously specified priority structure. We apply our results to characterize efficient deferred acceptance rules. 1.

The random priority (random serial dictatorship) mechanism is a common method for assigning objects. The mechanism is easy to implement and strategy-proof. However, this mechanism is inefficient, because all agents may be made better off by another mechanism that increases their chances of obtaining more preferred objects. This form of inefficiency is eliminated by a mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications is an open question. We show that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.

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 give two characterizations of Pareto optimality via “near” weighted utilitarian welfare maximization. One characterization sequentially maximizes utilitarian welfare functions using a finite sequence of nonnegative and eventually positive welfare weights. The other maximizes a utilitarian welfare function with a certain class of positive hyperreal weights. The social welfare ordering represented by these “near” weighted utilitarian welfare criteria is characterized by the standard axioms for weighted utilitarianism under a suitable weakening of the continuity axiom.