On the Core of Multiple Longest Traveling Salesman Games

CentER Discussion Paper No. 2003-127

18 Pages Posted: 16 Jul 2004

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

Herbert Hamers

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

Date Written: 2003

Abstract

In this paper, we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward. First, it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions. Secondly, it is shown that MLTS games with five or less players have a nonempty core. However, a six player MLTS game may have an empty core. For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.

Keywords: Game theory, longest traveling salesman problem/game, multiple longest traveling salesman problem/game, core

Suggested Citation

Estevez-Fernandez, Arantza and Borm, Peter E. M. and Hamers, Herbert, On the Core of Multiple Longest Traveling Salesman Games (2003). CentER Discussion Paper No. 2003-127. Available at SSRN: https://ssrn.com/abstract=556969 or http://dx.doi.org/10.2139/ssrn.556969

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

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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