Abstract
Abstract Duality theorems for assignment models are usually derived assuming countable additivity of the assignment and the population measures. In this paper, we use finitely additive measures to model assignments of buyers and sellers. This relaxation results in more complete duality theorems and gives greater flexibility concerning the existence of solutions, assumptions on the spaces of agents and on profit functions. We treat two modifications of the nonatomic assignment model. In the first model, upper and lower bounds are imposed on the marginal measures representing the activities of the buyers and sellers where the lower bounds reflect a certain minimum required level of activity on the agents. In the second model, the interaction of the agents is further restricted to a certain specified subset of all matchings of buyers and sellers.
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Ramachandran, D., Rüschendorf, L. (2002). Assignment Models for Constrained Marginals and Restricted Markets. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_21
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DOI: https://doi.org/10.1007/978-94-017-0061-0_21
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