Public Congestion Network Situations, and Related Games
AbstractThis paper analyzes congestion effects on network situations from a cooperative game theoretic perspective. In network situations players have to connect themselves to a source. Since we consider publicly available networks any group of players is allowed to use the entire network to establish their connection. We deal with the problem of finding an optimal network, the main focus of this paper is however to discuss the arising cost allocation problem. For this we introduce two different transferable utility cost games. For concave cost functions we use the direct cost game, where coalition costs are based on what a coalition can do in absence of other players. This paper however mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three egalitarian principles, and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-58.
Date of creation: 2007
Date of revision:
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Congestion; network situations; cooperative games; public;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-09-16 (All new papers)
- NEP-GTH-2007-09-16 (Game Theory)
- NEP-NET-2007-09-16 (Network Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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"Operations research games: A survey,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-305110, Tilburg University.
- Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
- Quant, M. & Borm, P.E.M. & Reijnierse, J.H., 2003.
"Congestion Network Problems and Related Games,"
2003-106, Tilburg University, Center for Economic Research.
- Quant, M. & Reijnierse, J.H., 2004. "Convex Congestion Network Problems," Discussion Paper 2004-59, Tilburg University, Center for Economic Research.
- Matsubayashi, Nobuo & Umezawa, Masashi & Masuda, Yasushi & Nishino, Hisakazu, 2005. "A cost allocation problem arising in hub-spoke network systems," European Journal of Operational Research, Elsevier, vol. 160(3), pages 821-838, February.
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