Sequencing Games with Repeated Players

CentER Discussion Paper Series No. 2004-128

16 Pages Posted: 5 Jan 2005

See all articles by Arantza Estevez-Fernandez

Arantza Estevez-Fernandez

VU University Amsterdam - Department of Econometrics and Operations Research; Tinbergen Institute

Peter Borm

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

Pedro Calleja

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics

Herbert Hamers

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

Date Written: December 2004

Abstract

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP (repeated player) sequencing situations. In max-RP sequencing situations it is assumed that each player's cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing games. Moreover, it is seen that min-RP sequencing games are convex.

Keywords: Cooperative game theory, sequencing, equal gain splitting, core, convexity

JEL Classification: C71

Suggested Citation

Estevez-Fernandez, Arantza and Borm, Peter E. M. and Calleja, Pedro and Hamers, Herbert, Sequencing Games with Repeated Players (December 2004). CentER Discussion Paper Series No. 2004-128. Available at SSRN: https://ssrn.com/abstract=642423 or http://dx.doi.org/10.2139/ssrn.642423

Arantza Estevez-Fernandez (Contact Author)

VU University Amsterdam - Department of Econometrics and Operations Research ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Peter E. M. Borm

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

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Pedro Calleja

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics ( email )

Avda. Diagonal 690
Barcelona, 08034
Spain

Herbert Hamers

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

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