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On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game

R. Pablo Arribillaga (), Jordi Masso and Alejandro Neme ()

UFAE and IAE Working Papers from Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC)

Abstract: We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with 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 to 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 ma- trices 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.

Keywords: Assignment Game; Competitive Equilibrium; Core; Group Stability. (search for similar items in EconPapers)
JEL-codes: C78 D78 (search for similar items in EconPapers)
Pages: 36
Date: 2013-12-09
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Journal Article: On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game (2014) Downloads
Working Paper: On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game (2013) Downloads
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