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

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

*Journal of Applied Mathematics*, 2014, vol. 2014, 1-20

**Abstract:**

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.

**Date:** 2014

**References:** Add references at CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://downloads.hindawi.com/journals/JAM/2014/190614.pdf (application/pdf)

http://downloads.hindawi.com/journals/JAM/2014/190614.xml (text/xml)

**Related works:**

Working Paper: On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game (2013)

Working Paper: On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game (2013)

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:hin:jnljam:190614

**DOI:** 10.1155/2014/190614

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi

Bibliographic data for series maintained by Mohamed Abdelhakeem ().