On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/190614 |
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| _version_ | 1832562139705901056 |
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| author | R. Pablo Arribillaga Jordi Massó Alejandro Neme |
| author_facet | R. Pablo Arribillaga Jordi Massó Alejandro Neme |
| author_sort | R. Pablo Arribillaga |
| collection | DOAJ |
| description | We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view. |
| format | Article |
| id | doaj-art-eacbffc38b9c410495cb713d0ad76451 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-eacbffc38b9c410495cb713d0ad764512025-02-03T01:23:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/190614190614On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment GameR. Pablo Arribillaga0Jordi Massó1Alejandro Neme2Instituto de Matemática Aplicada San Luis (UNSL-CONICET), Ejército de los Andes 950, 5700 San Luis, ArgentinaDepartament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona and Barcelona GSE, Edifici B, Bellaterra, 08193 Barcelona, SpainInstituto de Matemática Aplicada San Luis (UNSL-CONICET), Ejército de los Andes 950, 5700 San Luis, ArgentinaWe study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.http://dx.doi.org/10.1155/2014/190614 |
| spellingShingle | R. Pablo Arribillaga Jordi Massó Alejandro Neme On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game Journal of Applied Mathematics |
| title | On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game |
| title_full | On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game |
| title_fullStr | On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game |
| title_full_unstemmed | On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game |
| title_short | On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game |
| title_sort | on the structure of cooperative and competitive solutions for a generalized assignment game |
| url | http://dx.doi.org/10.1155/2014/190614 |
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