Cooperative Newsvendor Games: A Review

  • Luigi Montrucchio
  • Henk Norde
  • Ulaş Özen
  • Marco Scarsini
  • Marco Slikker
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 176)


In this survey, we review some of the main contributions to the cooperative approach of newsvendor situations. We show how newsvendor situations with several retailers can be modeled as a transferable-utility cooperative game and we concentrate on one solution concept: the core. First, we examine the basic model and then we consider several variations that are of interest from a theoretical and an applied viewpoint.


Newsvendor model Core Shapley value Large games Multiple warehouses Transshipment costs Stochastic programming Duality 


  1. Anily, S., & Haviv, M. (2010). Cooperation in service systems. Operations Research, 58(3): 660–673.CrossRefGoogle Scholar
  2. Anupindi, R., & Bassok, Y. (1999). Centralization of stocks: retailers vs. manufacturer. Management Science, 45(2), 178–191.Google Scholar
  3. Anupindi, R., Bassok, Y., & Zemel, E. (2001). A general framework for the study of decentralized distribution systems. Manufacturing & Service Operations Management, 3(4), 349–368.CrossRefGoogle Scholar
  4. Aumann, R. J. (1959). Acceptable points in general cooperative n-person games. In A. Tucker & R. Luce (Eds.), Contributions to the theory of games IV (pp. 287–324). Princeton: Princeton University Press.Google Scholar
  5. Bondareva, O. N. (1963). Some applications of the methods of linear programming to the theory of cooperative games. Problemy Kibernet., 10, 119–139.Google Scholar
  6. Burer, S., & Dror, M. (2011). Newsvendor games: convex optimization of centralized inventory operations. TOP. forthcoming.Google Scholar
  7. Cachon, G., & Netessine, S. (2004). Game theory in supply chain analysis. In D. Simchi-Levi, S. D. Wu, & M. Shen (Eds.), Handbook of quantitative supply chain analysis: Modeling in the e-business era. Berlin: Springer.Google Scholar
  8. Chen, X. (2009). Inventory centralization games with price-dependent demand and quantity discount. Operations Research, 57(6), 1394–1406.CrossRefGoogle Scholar
  9. Chen, X., & Zhang, J. (2009). A stochastic programming duality approach to inventory centralization games. Operations Research, 57(4), 840–851.CrossRefGoogle Scholar
  10. Chwe, M. S.-Y. (1994). Farsighted coalitional stability. Journal of Economics Theory, 63, 299–325.CrossRefGoogle Scholar
  11. Crawford, V. (1998). A survey of experiments on communication via cheap talk. Journal of Economics Theory, 78, 286–298.CrossRefGoogle Scholar
  12. Crawford, V., & Sobel, J. (1982). Strategic information transmission. Econometrica, 50, 1431–1451.CrossRefGoogle Scholar
  13. Dror, M., Guardiola, L. A., Meca, A., & Puerto, J. (2008). Dynamic realization games in newsvendor inventory centralization. International Journal of Game Theory, 37(1), 139–153.CrossRefGoogle Scholar
  14. Dror, M., & Hartman, B. C. (2007). Shipment consolidation: who pays for it and how much? Management Science, 53(1), 78–87.CrossRefGoogle Scholar
  15. Dror, M., & Hartman, B. C. (2011). Survey of cooperative inventory games and extensions. Journal of the Operations Research Society, 62(4), 565–580.CrossRefGoogle Scholar
  16. Eppen, G. D. (1979). Effect of centralization on expected cost in a multi-location newsboy problem. Management Science, 25, 498–501.CrossRefGoogle Scholar
  17. Fiestras-Janeiro, M., García-Jurado, I., Meca, A., & Mosquera, M. (2011). Cooperative game theory and inventory management. European Journal Operations Research, 210, 459–466.CrossRefGoogle Scholar
  18. Gerchak, Y., & Gupta, D. (1991). On apportioning costs to customers in centralized continuous review inventory systems. Journal of Operations Management, 10, 546–551.CrossRefGoogle Scholar
  19. Granot, D., & Sošić, G. (2003). A three-stage model for a decentralized distribution system of retailers. Operations Research, 51(5), 771–784.CrossRefGoogle Scholar
  20. Hanany, E., & Gerchak, Y. (2008). Nash bargaining over allocations in inventory pooling contracts. Naval Research Logistics, 55(6), 541–550.CrossRefGoogle Scholar
  21. Hartman, B. C. (1994). Cooperative games and inventory cost allocation. PhD thesis, University of Arizona.Google Scholar
  22. Hartman, B. C., & Dror, M. (1996). Cost allocation in continuous review inventory models. Naval Research Logistics, 43(1), 549–561.CrossRefGoogle Scholar
  23. Hartman, B. C., & Dror, M. (2003). Optimizing centralized inventory operations in a cooperative game theory setting. IIE Transactions, 35(3), 243–257.CrossRefGoogle Scholar
  24. Hartman, B. C., & Dror, M. (2005). Allocation of gains from inventory centralization in newsvendor environments. IIE Transactions, 37(2), 93–107.CrossRefGoogle Scholar
  25. Hartman, B. C., Dror, M., & Shaked, M. (2000). Cores of inventory centralization games. Games and Economic Behavior, 31(1), 26–49.CrossRefGoogle Scholar
  26. Ichiishi, T. (1990). Comparative cooperative game theory. International Journal of Game Theory, 19(2), 139–152.CrossRefGoogle Scholar
  27. Kannai, Y. (1969). Countably additive measures in cores of games. Journal of Mathematical Analysis and Applications, 27, 227–240.CrossRefGoogle Scholar
  28. Kemahlioğlu-Ziya, E., & Bartholdi, J. (2011). Centralizing inventory in supply chains by using shapley value to allocate the profits. Manufacturing & Service Operations Management, 13, 146–162.CrossRefGoogle Scholar
  29. Lehrer, E. (2002). Allocation processes in cooperative games. International Journal of Game Theory, 31(3), 341–351.CrossRefGoogle Scholar
  30. Leng, M., & Parlar, M. (2005). Game theoretic applications in supply chain management: a review. INFOR Information Systems and Operational Research, 43(3), 187–220.Google Scholar
  31. Marinacci, M., & Montrucchio, L. (2004). Introduction to the mathematics of ambiguity. In I. Gilboa (Ed.), Uncertainty in economic theory, (pp. 46–107). London: Routledge.CrossRefGoogle Scholar
  32. Maskin, E., & Riley, M. (1984). Monopoly with incomplete information. Rand Journal of Economics, 15, 171–196.CrossRefGoogle Scholar
  33. Montrucchio, L., & Scarsini, M. (2007). Large newsvendor games. Games and Economic Behavior, 58(2), 316–337.CrossRefGoogle Scholar
  34. Müller, A., Scarsini, M., & Shaked, M. (2002). The newsvendor game has a nonempty core. Games and Economic Behavior, 38(1), 118–126.CrossRefGoogle Scholar
  35. Nagarajan, M., & Sošić, G. (2008). Game-theoretic analysis of cooperation among supply chain agents: review and extensions. European Journal Operations Research, 187(3), 719–745.CrossRefGoogle Scholar
  36. Özen, U., Erkip, N., & Slikker, M. (2012a). Stability and monotonicity in newsvendor situations. European Journal Operations Research, 218(2), 416-425.CrossRefGoogle Scholar
  37. Özen, U., Fransoo, J., Norde, H., & Slikker, M. (2008). Cooperation between multiple newsvendors with warehouses. Manufacturing & Service Operations Management, 10(2), 311–324.CrossRefGoogle Scholar
  38. Özen, U., Norde, H., & Slikker, M. (2011). On the convexity of newsvendor games. International Journal of Production Economics, 133(1), 35–42.CrossRefGoogle Scholar
  39. Özen, U., Slikker, M., & Norde, H. (2009). A general framework for cooperation under uncertainty. Operations Research Letters, 37(3), 148–154.CrossRefGoogle Scholar
  40. Özen, U., Sošić, G., & Slikker, M. (2012b). A multi-retailer decentralized distribution system with updated demand information. European Journal Operations Research, 216, 573–583.CrossRefGoogle Scholar
  41. Özer, O., Zheng, Y., & Chen, K. (2011). Trust in forecast information sharing. Management Science, 57, 1111–1137.CrossRefGoogle Scholar
  42. Parlar, M. (1988). Game theoretic analysis of the substitutable product inventory problem with random demands. Naval Research Logistics, 35(3), 397–409.CrossRefGoogle Scholar
  43. Peleg, B., & Sudhölter, P. (2007). Introduction to the theory of cooperative games (2nd ed.). Berlin: Springer.Google Scholar
  44. Puccetti, G., & Scarsini, M. (2010). Multivariate comonotonicity. Journal of Multivariate Analysis, 101(1), 291–304.CrossRefGoogle Scholar
  45. Ren, Z., Cohen, M., Ho, T., & Terwiesch, C. (2010). Information sharing in a long-term supply chain relationship: the role of customer review strategy. Operations Research, 58, 81–93.CrossRefGoogle Scholar
  46. Robinson, L. W. (1993). A comment on Gerchak and Gupta’s “on apportioning costs to customers in centralized continuous review inventory systems”. Journal of Operations Management, 11, 99–102.CrossRefGoogle Scholar
  47. Rockafellar, R. T., & Wets, R. J.-B. (1976). Stochastic convex programming: relatively complete recourse and induced feasibility. SIAM Journal Control Optimization, 14(3), 574–589.CrossRefGoogle Scholar
  48. Schmeidler, D. (1967). On balanced games with infinitely many players. Technical report, Department of Mathematics, The Hebrew University of Jerusalem. Research program in game theory and mathematical economics, research memorandum no. 28.Google Scholar
  49. Schmeidler, D. (1969). The nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 17, 1163–1170.CrossRefGoogle Scholar
  50. Schmeidler, D. (1972). Cores of exact games. I. Journal of Mathematical Analysis and Applications, 40, 214–225.Google Scholar
  51. Shapley, L. S. (1953). A value for n-person games. In Contributions to the theory of games, vol. 2, Annals of mathematics studies (vol. 28, pp. 307–317). Princeton, NJ: Princeton University Press.Google Scholar
  52. Shapley, L. S. (1967). On balanced sets and cores. Naval Research Logistics Quarterly, 14, 453–460.CrossRefGoogle Scholar
  53. Shapley, L. S. (1971). Cores of convex games. International Journal of Game Theory, 1, 11–26.CrossRefGoogle Scholar
  54. Slikker, M., Fransoo, J., & Wouters, M. (2001). Joint ordering in multiple news-vendor situations: a game-theoretical approach. Technical report, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar
  55. Slikker, M., Fransoo, J., & Wouters, M. (2005). Cooperation between multiple news-vendors with transshipments. European Journal Operations Research, 167(2), 370–380.CrossRefGoogle Scholar
  56. Sošić, G. (2006). Transshipment of inventories among retailers: myopic versus farsighted stability. Management Science, 52, 1493–1508.CrossRefGoogle Scholar
  57. Wang, Q., & Parlar, M. (1994). A three-person game theory model of the substitutable product inventory problem with random demands. European Journal Operations Research, 76, 83–97.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Luigi Montrucchio
    • 1
  • Henk Norde
    • 2
  • Ulaş Özen
    • 3
  • Marco Scarsini
    • 4
  • Marco Slikker
    • 5
  1. 1.Dipartimento di Statistica e Matematica Applicata and Collegio Carlo AlbertoUniversità di TorinoTorinoItaly
  2. 2.Center and Department of Econometrics and ORTilburg UniversityTilburgNetherlands
  3. 3.Alcatel-Lucent, Bell Labs IrelandDublin 15Ireland
  4. 4.Dipartimento di Economia e FinanzaLUISSRomaItaly
  5. 5.School of Industrial EngineeringTechnische Universiteit EindhovenEindhovenNetherlands

Personalised recommendations