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Large newsvendor games

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  • Montrucchio, Luigi
  • Scarsini, Marco

Abstract

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. A similar game (modeled in terms of costs) was considered by Muller et al. (2002), who proved that this game is balanced for every possible joint distribution of the random demands. In this paper we consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increases.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 58 (2007)
Issue (Month): 2 (February)
Pages: 316-337

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Handle: RePEc:eee:gamebe:v:58:y:2007:i:2:p:316-337

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Ula\c{s} Özen & Jan Fransoo & Henk Norde & Marco Slikker, 2008. "Cooperation Between Multiple Newsvendors with Warehouses," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 311-324, February.
  2. Milchtaich, Igal, 1998. "Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 25-46, July.
  3. Slikker, Marco & Fransoo, Jan & Wouters, Marc, 2005. "Cooperation between multiple news-vendors with transshipments," European Journal of Operational Research, Elsevier, vol. 167(2), pages 370-380, December.
  4. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier.
  5. Kannai, Yakar, 1972. "Continuity Properties of the Core of a Market: A Correction," Econometrica, Econometric Society, vol. 40(5), pages 955-58, September.
  6. Gérard P. Cachon & Martin A. Lariviere, 1999. "Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance," Management Science, INFORMS, vol. 45(8), pages 1091-1108, August.
  7. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  8. Diego Moreno & Benyamin Shitovitz & Ezra Einy, 1999. "The core of a class of non-atomic games which arise in economic applications," International Journal of Game Theory, Springer, vol. 28(1), pages 1-14.
  9. Hartman, Bruce C. & Dror, Moshe & Shaked, Moshe, 2000. "Cores of Inventory Centralization Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 26-49, April.
  10. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
  11. Debreu, Gerard, 1975. "The rate of convergence of the core of an economy," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 1-7, March.
  12. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
  13. Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
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Cited by:
  1. Ozen, U. & Norde, H.W. & Slikker, M., 2005. "On the Convexity of News Vendor Games," Discussion Paper 2005-103, Tilburg University, Center for Economic Research.
  2. Ozen, U. & Slikker, M. & Norde, H.W., 2007. "A General Framework for Cooperation under Uncertainty," Discussion Paper 2007-57, Tilburg University, Center for Economic Research.
  3. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2011. "Cooperative game theory and inventory management," European Journal of Operational Research, Elsevier, vol. 210(3), pages 459-466, May.

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