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Network flow problems and permutationally concave games

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  • Trudeau, Christian

Abstract

We examine network problems where agents have to be connected to a source in order to obtain goods, and in which costs on different arcs are a function of the flow of goods. When all cost functions are concave, the resulting game might have an empty core. We introduce a set of problems with concave functions, called the ordered quasi-symmetric congestion problems. We show that they generate permutationally concave games, a weakening of the concept of concavity, that ensures non-emptiness of the core.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 1 (July)
Pages: 121-131

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:121-131

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Stability Core Network Concavity;

References

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  1. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  2. Quant, Marieke & Borm, Peter & Reijnierse, Hans, 2006. "Congestion network problems and related games," European Journal of Operational Research, Elsevier, vol. 172(3), pages 919-930, August.
  3. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
  4. Meca, Ana & Timmer, Judith & Garcia-Jurado, Ignacio & Borm, Peter, 2004. "Inventory games," European Journal of Operational Research, Elsevier, vol. 156(1), pages 127-139, July.
  5. Bhaskar Dutta & Anirban Kar, 2002. "Cost monotonicity, consistency and minimum cost spanning tree games," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 02-04, Indian Statistical Institute, New Delhi, India.
  6. Willard I. Zangwill, 1968. "Minimum Concave Cost Flows in Certain Networks," Management Science, INFORMS, vol. 14(7), pages 429-450, March.
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Cited by:
  1. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.

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