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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 ()

No 740, Working Papers from Barcelona Graduate School of Economics

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 alternative 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 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.

Keywords: assignment game; Competitive Equilibrium; core; group stability (search for similar items in EconPapers)
JEL-codes: C78 D78 (search for similar items in EconPapers)
Date: 2013-10
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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Related works:
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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