On the Core of Multiple Longest Traveling Salesman Games
AbstractIn 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 ¯ve 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2003-127.
Date of creation: 2003
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Web page: http://center.uvt.nl
game theory; traveling salesman problem; games; core;
Other versions of this item:
- Estevez-Fernandez, Arantza & Borm, Peter & Hamers, Herbert, 2006. "On the core of multiple longest traveling salesman games," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1816-1827, November.
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- Estevez Fernandez, M.A. & Borm, P.E.M. & Meertens, M. & Reijnierse, J.H., 2006.
"On the Core of Routing Games with Revenues,"
2006-43, Tilburg University, Center for Economic Research.
- Grabisch, Michel & Li, Tong, 2011.
"On the set of imputations induced by the k-additive core,"
European Journal of Operational Research,
Elsevier, vol. 214(3), pages 697-702, November.
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