The Nonatomic Assignment Model
We formulate a model with a continuum of individuals to be assigned to a continuum of different positions which is an extension of the finite housing market version due to Shapley and Shubik. We show that optimal solutions to such a model exist and have properties similar to those established for finite models, namely, an equivalence among the following: (1) optimal solutions to the linear programming problem (and its dual) associated with the assignment model; (2) the core of the associated market game; and (3) the Walrasian equilibria of the associated market economy.
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