We study two-sided in which agents are buyers and sellers or firms and workers or men and women. The agents are to form partnerships (which provide them with satisfaction) and at the same time make monetary transfers (e.g. salaries or dowries). The core of this market game is shown to have a particularly nice structure so that precise answers can be given to questions concerning comparative statics and manipulability. THE IDEA OF USING Walrasian equilibrium as a mechanism for making allocations with desirable properties of fairness and efficiency has been studied extensively. The scheme involves having agents specify their supply and demand functions. The competitive equilibria are then calculated and allocations are made accordingly. In general this procedure may run into two difficulties: first, nonuniqueness-if there are several equilibria there may be no fair way to decide which one should be implemented; and second, manipulability-if there is only one equilibrium an informed agent may be able to influence it by suitably falsifying his demand data. However, as we will show here, using the Walrasian mechanism does work remarkably well for a certain class of important markets. These are the matching markets of our title and they include for single items, like houses, where it is assumed that traders do not wish to acquire more than one item. They also include labor in which it is desired to match workers with jobs at suitable salaries, academic markets in which students are to be assigned to educational institutions, marriage markets where men and women are matched through negotiating of dowries. It turns out that in these both the problems of nonuniqueness and manipulability can be resolved in a

In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment of important topics in mathematical economics which can be analyzed by linear models. This self-contained work requires few mathematical prerequisites and provides all necessary groundwork in the first few chapters. After introducing basic geometric concepts of vectors and vector spaces, Gale proceeds to give the main theorems on linear inequalities?theorems underpinning the theory of games, linear programming, and the Neumann model of growth. He then explores such subjects as linear programming; the theory of two-person games; static and dynamic theories of linear exchange models, including problems of equilibrium prices and dynamic stability; and methods of play, optimal strategies, and solutions of matrix games. This book should prove an invaluable reference source and text for mathematicians, engineers, economists, and those in many related areas.

A set of n objects and an amount M of money is to be distributed among m people. Example: the objects are tasks and the money is compensation from a fixed budget. An elementary argument via constrained optimization shows that for M sufficiently large the set of efficient, envy free allocations is nonempty and has a nice structure. In particular, various criteria of justice lead to unique best fair allocations that are well behaved with respect to changes of M. This is in sharp contrast to the usual fair division theory with divisible goods. Copyright 1991 by The Econometric Society.

A collection of items is to be distributed among several bidders, and each bidder is to receive at most one item. Assuming that the bidders place some monetary value on each of the items, it has been shown that there is a unique vector of equilibrium prices that is optimal, in a suitable sense, for the bidders. In this paper we describe two dynamic auction mechanisms: one achieves this equilibrium and the other approximates it to any desired degree of accuracy.

A collection of items is to be distributed among several bidders, and each bidder is to receive at most one item. Assuming that the bidders place some monetary value on each of the items, it has been shown that there is a unique vector of equilibrium prices that is optimal, in a suitable sense, for the bidders. In this paper we describe two dynamic auction mechanisms: one achieves this equilibrium and the other approximates it to any desired degree of accuracy.