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The nonatomic assignment model. (English) Zbl 0808.90021
Summary: 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: (i) optimal solutions to the linear programming problem (and its dual) associated with the assignment model; (ii) the core of the associated market game; (iii) the Walrasian equilibria of the associated market economy.

MSC:
91B50 General equilibrium theory
90C05 Linear programming
91A40 Other game-theoretic models
49J52 Nonsmooth analysis
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