Assignment Situations with Multiple Ownership and Their Games

International Game Theory Review, Vol. 11, Issue 1, pp. 1-13, 2009

Posted: 28 Oct 2009

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: March 2009

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 Shubik (1972) introduced a class of assignment games.

This paper introduces assignment situations with multiple ownership (AMO). In these situations an object can be owned by several agents and an agent can participate in the ownership of more than one object. For AMO situations we introduce the class of k-AMO games. An AMO situation is called balanced if for any choice of the reward matrix the corresponding 1-AMO game is balanced. We provide necessary and sufficient conditions for balancedness of AMO situations. Moreover, sufficient conditions are provided for balancedness of k-AMO games.

Keywords: Assignment situations, matchings, assignment games, balancedness

Suggested Citation

Miquel, Sylvia and Velzen, Bas van and Hamers, Herbert and Norde, Henk W., Assignment Situations with Multiple Ownership and Their Games (March 2009). International Game Theory Review, Vol. 11, Issue 1, pp. 1-13, 2009. Available at SSRN: https://ssrn.com/abstract=1495587

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

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
281
PlumX Metrics