Assignment Situations with Multiple Ownership and Their Games

CentER Discussion Paper No. 2005-78

Posted: 11 Jul 2005

See all articles by Sylvia Miquel

Sylvia Miquel

University of Lleida - Department of Mathematics

Bas van Velzen

affiliation not provided to SSRN

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Henk Norde

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research

Multiple version iconThere are 2 versions of this paper

Date Written: June 2005

Abstract

An assignment situation can be considered as a two-sided market consisting of two disjoint sets of objects. A non-negative reward matrix describes the profit if an object of one group is assigned to an object of the other group. Assuming that each object is owned by a different agent, Shapley and Shubnik (1972) introduced a class of assignment games arising from these assignement situations.

This paper introduces assignment situations with multiple ownership. In these situations, each object can be owned by several agents and each agent can participate in the ownership of more than one object. In this paper, we study simply assignment games and relaxations that arise from assignment situations with multiple ownership. First, necessary and sufficient conditions are provided for balanced assignment situations with multiple ownership. An assignment situation with multiple ownership is balanced if for any choice of the reward matrix the corresponding simple assignment game is balanced. Second, balancedness results are obtained for relaxations of simple assignments games.

Keywords: Assignment situations, matchings, assignment games, balancedness

JEL Classification: C71

Suggested Citation

Miquel, Sylvia and Velzen, Bas van and Hamers, Herbert and Norde, Henk W., Assignment Situations with Multiple Ownership and Their Games (June 2005). CentER Discussion Paper No. 2005-78. Available at SSRN: https://ssrn.com/abstract=756305

Sylvia Miquel

University of Lleida - Department of Mathematics ( email )

Carrer Jaume II
69 Campus Cappont
Lleida, Catalunya E-25001
Spain

Bas van Velzen

affiliation not provided to SSRN ( email )

No Address Available

Herbert Hamers (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Henk W. Norde

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 3245 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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