Strongly Essential Coalitions and the Nucleolus of Peer Group Games

CentER Working Paper No. 2003-19

Posted: 26 May 2004

See all articles by Rodica Branzei

Rodica Branzei

'A.l. Cuza' University of Iasi, Romania - Faculty of Computer Sciences

Tamas Solymosi

Corvinus University of Budapest

Stef H. Tijs

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research; Università degli Studi di Genova - Dipartimento di Matematica

Date Written: 2003

Abstract

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n-1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.

Keywords: Cooperative game, peer group game, nucleolus, kernel, computation

JEL Classification: C71

Suggested Citation

Branzei, Rodica and Solymosi, Tamas and Tijs, Stef H., Strongly Essential Coalitions and the Nucleolus of Peer Group Games (2003). CentER Working Paper No. 2003-19, Available at SSRN: https://ssrn.com/abstract=550164

Rodica Branzei (Contact Author)

'A.l. Cuza' University of Iasi, Romania - Faculty of Computer Sciences ( email )

Carol I Blvd, Nr.11
Iasi
Romania

Tamas Solymosi

Corvinus University of Budapest ( email )

1828 Budapest
Pf. 489
Hungary
36-1-217 4505 (Phone)

Stef H. Tijs

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
B925
5000 LE Tilburg
Netherlands
+31 13 466 2348 (Phone)

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

Tilburg, 5000 LE
Netherlands

Università degli Studi di Genova - Dipartimento di Matematica

Via Dodecaneso 35
16146 Genoa
Italy

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