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Game Theory Models and Their Applications in Inventory Management and Supply Chain

  • Altannar Chinchuluun
  • Athanasia Karakitsiou
  • Athanasia Mavrommati
Part of the Springer Optimization and Its Applications book series (SOIA, volume 17)

Analysis of supply chain politics can benefit from applying game-theory concepts extensively. Game theory tries to enlighten the interactions between individuals or groups of people whose goals are opposed conflicting, or at least partially competing. In this chapter, we review classic game theoretical approaches to modeling and solving certain problems in supply chain management. Both noncooperative and cooperative models are discussed and solution procedures are presented in single-period and multiperiod settings. As used here, a “game” is a metaphor for any interaction among the decision makers in a supply chain.

Keywords

inventory supply chain noncooperative games cooperative games Nash equilibrium Stackelberg game transferable utility core bargaining biform games 

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References

  1. 1.
    Anand, K., Anupindi, R., Bassok, Y.: Strategic Inventories in Procurement Contracts. University of Pennsylvania, working paper (2002)Google Scholar
  2. 2.
    Anupindi, R., Bassok, Y.: Centralization of Stocks: Retailers vs. Manufacturer. Management Science, 45(2), 178–191 (1999)CrossRefGoogle Scholar
  3. 3.
    Anupindi, R., Bassok, Y., Zemel, E.: A General Framework for the Study of Decentralized Distribution Systems. Manufacturing & Service Operations Management, 3, 349–368 (2001)CrossRefGoogle Scholar
  4. 4.
    Avsar, Z.M., Baykal-Gürsoy, M.: Inventory Control under Substitutable Demand: A Stochastic Game Application. Naval Research Logistics, 49, 359–375 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Basar, T., Oldser, G.J.: Dynamics Noncooperative Game Theory. In: Ames, W.F. (eds) Mathematics in Science and Engineering. Vol. 160, Academic Press, New York (1982)Google Scholar
  6. 6.
    Bernstein, F., Marx, L.: Reservation Profit Levels and the Division of Supply Chain Profit. Duke University, working paper (2004)Google Scholar
  7. 7.
    Binmore, K.G., Runbinstein, A., Wolinsky, A.: The Nash Bargaining Solution in Economic Modelling, Rand Journal of Economics, 17, 176–188 (1986)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Binmore, K.G., Shaked, A., Sutton, J.: An Outside Option Experiment. Quarterly Journal of Economics, 104, 753–770 (1988)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bondareva, O.: Some Applications of Linear Programming Methods to the Theory of Cooperative Games (in Russian). Problemi Kibernet, 10, 119–139 (1963)MathSciNetGoogle Scholar
  10. 10.
    Brandenburger, A., Stuart, H.W.: Biform Games. Columbia University (revised August 2004), working paper (2003)Google Scholar
  11. 11.
    Cachon, G.P.: Competitive and Cooperative Inventory Management in a Two-Echelon Supply Chain with Lost Sales. The Fuqua School of Business, Dyke University, working paper (1999)Google Scholar
  12. 12.
    Cachon, G.P.: Stock Wars: Inventory Competition in a Two-Echelon Supply Chain. Operations Research, 49, 658–674 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Cachon, G.P: Supply Chain with Contracts. In: Graves, S., de Kok, T. (eds) Handbooks in Operations Research and Management Science: Supply Chain Management. North-Holland, Amsterdam, 229–340 (2003)Google Scholar
  14. 14.
    Cachon, G.P: The Allocation of Inventory Risk in a Supply Chain: Push, Pull and Advanced Purchase Discount Contracts. Management Science, 50, 222–238 (2004)CrossRefGoogle Scholar
  15. 15.
    Cachon, G., Lariviere, M.A.: Supply Chain Coordination with Revenue Sharing Contracts: Strengths and Limitations. Management Science, 51, 30–44 (2005)CrossRefGoogle Scholar
  16. 16.
    Cachon, G.P., Lariviere, M.: Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance. Management Science, 45, pp. 1091–1108 (1999)CrossRefGoogle Scholar
  17. 17.
    Cachon, G.P., Lariviere, M.A.: An Equilibrium Analysis of Linear, Proportional and Uniform Allocation of Scarce Capacity. IIE Transactions, 31, 835–849 (1999)Google Scholar
  18. 18.
    Cachon, G.P., Netessine, S.: Game Theory in Supply Chain Analysis. In: Simchi-Levi, D., Wu, S.D., Shen, Z.M. (eds) Handbook of Quantitative. Supply Chain Analysis: Modeling in the E-Business Era. Kluwer Academic Publishers, New York 13–65 (2004)Google Scholar
  19. 19.
    Cachon, G.P., Zipkin, P.H. Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain. Management Science, 45, 936–53 (1999)CrossRefGoogle Scholar
  20. 20.
    Chae, S., Heidhues, P.: The Effects of Downstream Distributor Chains on Upstream Producer Entry: A Bargaining Perspective, Discussion Paper FS IV 99 - 35, Wissenschaftszentrum Berlin. (1999)Google Scholar
  21. 21.
    Chand, S., Ward, J.E., Weng, Z.K.: A Parts Selection Model with One-Way Substitution. European Journal of Operational Research, 73, 65–69 (1994)zbMATHCrossRefGoogle Scholar
  22. 22.
    Chen, F. Decentralized Supply Chains Subject to Information Delays. Management Science, 45, 1076–1090 (1999)CrossRefGoogle Scholar
  23. 23.
    Chod, J., Rudi, N.: Strategic Investments, Trading and Pricing under Forecast Updating. University of Rochester, working paper (2003)Google Scholar
  24. 24.
    Clark, A., Scarf, H.: Optimal Policies for a Multi-Echelon Inventory Problem. Management Science, 6, 475–490 (1960)CrossRefGoogle Scholar
  25. 25.
    Colman, A.M.: Game Theory and Its application. Routledge, New York (1999)Google Scholar
  26. 26.
    Dai, Y.: Game Theoretic Approach to Supply Chain Management. PhD Dissertation, North Carolina State University, Raleigh, NC (2003)Google Scholar
  27. 27.
    Dasgupta, P., Maskin, E.: The Existence of Equilibrium in Discontinuous Economic Games. 1: Theory. Review of Economics Studies, 53, pp. 1–26 (1986)Google Scholar
  28. 28.
    de Fontenay, C.C., Gans, J.S.: Vertical Integration in the Presence of Upstream Competition. Melbourne Business School and Department of Economics, University of Melbourne, working paper (2003)Google Scholar
  29. 29.
    Drezner, Z., Gurnani, H., Pasternack, B.A.: An EOQ Model with Substitutions Between Products. Journal of Operational Research Society, 46, 887–891 (1995)zbMATHCrossRefGoogle Scholar
  30. 30.
    Emmons, H., Gilbert, S.: Returns Policies in Pricing and Inventory Decision for Cataloque Goods. Management Science, 44, 276–283 (1998)zbMATHCrossRefGoogle Scholar
  31. 31.
    Eppen, G.D., Iyer, A.V.: Backup Agreements in Fashion Buying—the Value of Upstream Flexibility. Management Science, 43, 1469–1484 (1997)zbMATHCrossRefGoogle Scholar
  32. 32.
    Ertogral, K., Wu, S.D.: A Bargaining Game for Supply Chain Contracting. Lehigh University, Department of Industrial and Systems Engineering, Bethlehem, PA, working paper (2001)Google Scholar
  33. 33.
    Filar, J.A., Schultz, T.A., Thuijsman, F., Vrieze, D.J.: Nonlinear Programming and Stationary Equilibria in Stochastic Games. Mathematical Programming, 50, 227–238 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Gerchak, Y., Gupta, D.: Technical Note: On Apportioning Costs to Customers in Centralized Continuous Review Inventory Systems. Journal of Operations Management, 10, 546–551 (1991)CrossRefGoogle Scholar
  35. 35.
    Granot, D., Sosic, G.: A Three Stage Model for a Decentralized Distribution Systems of Retailers. Operations Research, 51(5), 771–784 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Hartman, B., Dror, M.: Cost Allocation in Continuous Review Inventory Models. Naval Research Logistic Quarterly, 43, 549–561 (1996)zbMATHCrossRefGoogle Scholar
  37. 37.
    Hartman, B., Dror, M., Shaked, M.: Cores of Inventory Centralization Games. Games and Economic Behavior, 31, 26–49 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  38. 38.
    Heyman, D.P., Sobel, M.J.: Stochastic Models in Operations Research. Vol. II: Stochastic Optimization, McGraw-Hill, New York (1984)zbMATHGoogle Scholar
  39. 39.
    Kalai, E., Smorodinsky, M.: Other Solutions to the Nash Bargaining Problem. Econometrica, 43, 513–518 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Khouja, M.: The Single-Period (News-Vendor) Problem: Literature Review and Suggestions for Future Research. Omega, 27, 537–553 (1999)CrossRefGoogle Scholar
  41. 41.
    Klastorin, T.D., Moinzadeh, K., Son, J.: Coordinating Orders in Supply Chains Through Price Discounts. IIE Transactions, 34, 679–689 (2002)Google Scholar
  42. 42.
    Kreps, M.D.: Game Theory and Economic Modelling. Oxford University Press, New York (2001)Google Scholar
  43. 43.
    Lariviere, M.A., Porteus, E.L.: Selling to the Newsvendor: An Analysis of Price-Only Contracts. Manufacturing & Service Operations Management, 3(4), 293–305 (2001)CrossRefGoogle Scholar
  44. 44.
    Lee, H., Whang, J.: Decentralized Multi-Echelon Supply Chains: Incentives and Information. Management Science, 45, 633–640 (1999)CrossRefGoogle Scholar
  45. 45.
    Lee, H., Padmanabhan, P., Whang, S.: Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science, 43, 546–558 (1997)zbMATHCrossRefGoogle Scholar
  46. 46.
    Lippman, S.A., McCardle, K.F.: The Competitive Newsboy. Operations Research, 45(1), 54–65 (1997)zbMATHCrossRefGoogle Scholar
  47. 47.
    Lucas, W.F.: An Overview of the Mathematical Theory of Games. Management Science, 18(5), 3–19 (1972)CrossRefMathSciNetGoogle Scholar
  48. 48.
    Mahajan, S., van Ryzin, G.J.: Inventory Competition Under Dynamic Consumer Choice. Operations Research, 49(5), 646–657 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Müller, A., Scarsini, M., Shaked, M.: The Newsvendor Game Has a Non-Empty Core. Games and Economic Behavior, 38, 118–126 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  50. 50.
    Muthoo, A.: On The Strategic Role of Outside Options in Bilateral Bargaining. Operations Research, 43, 292–297 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    Myerson, R.B.: Game Theory: Analysis of Conflicts. Harvard University Press, Boston (2002)Google Scholar
  52. 52.
    Nagarajan, M., Bassok, Y.: A Bargaining Framework in Supply Chains—the Assembly Problem. Marshall School of Business, University of Southern California, Los Angeles, CA, working paper (2002)Google Scholar
  53. 53.
    Napel, S.: Biletar Bargaining: Theory and Applications. Lecture Notes in Economics and Mathematical Systems, Vol. 518, Springer-Verlag, Heidelberg (2002)Google Scholar
  54. 54.
    Nash, J.F.: Equilibrium Points in n-Person Games. Proceedings of the National Academy of Sciences, 36, 48–49 (1950)zbMATHCrossRefMathSciNetGoogle Scholar
  55. 55.
    Nash, J.F.: The Bargaining Problem. Econometrica, 18, 155–162 (1950)CrossRefMathSciNetGoogle Scholar
  56. 56.
    Nash, J.F.: Non-Cooperative games. Annals of Mathematics, 54, 286–295 (1951)CrossRefMathSciNetGoogle Scholar
  57. 57.
    Netessine, S., Rudi, N.: Supply Chain Structures on the Internet and the Role of Marketing-Operations Interaction. In: Simchi-Levi, D., Wu, S.D., Shen, Z.M. (eds) Handbook of Quantitative. Supply Chain Analysis: Modeling in the E-Business Era. Kluwer Academic Publishers, New York, 607–639 (2004)Google Scholar
  58. 58.
    Netessine, S., Rudi, N.: Centralized and Competitive Inventory Models with Demand Substitution. Operations Research, 53, 329–335 (2003)CrossRefMathSciNetGoogle Scholar
  59. 59.
    Netessine, S., Rudi, N., Wang, Y.: Dynamic Inventory Competition and Customer Retention. working paper (2003)Google Scholar
  60. 60.
    Netessine, S., Shumsky, R.: Revenue Management Games: Horizontal and Vertical Competition. University of Pennsylvania, working paper (2001)Google Scholar
  61. 61.
    Osdorne, M.J., Rubinstein, A.: Bargaining and Markets. Academic Press, Inc., San Diego (1990)Google Scholar
  62. 62.
    Osdorne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge, Massachusetts (1994)Google Scholar
  63. 63.
    Parlar, M.: Game Theoretic Analysis of the Substitutable Product Inventory Problem with Random Demands. Naval Research Logistics, 35, 397–409 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  64. 64.
    Pasternack, P.: Optimal Pricing and Return Policies for Perishable Commodities. Marketing Science, 4, 998–1010 (1985)CrossRefGoogle Scholar
  65. 65.
    Plambeck, L.E., Terry, A.: Implications of Renegotiation for Optimal Contract Flexibility and Investment. Working Paper, Stanford University (2004)Google Scholar
  66. 66.
    Plambeck, L.E., Terry, A.: Sell the Plant? The Impact of Contract Manufacturing on Innovation, Capacity, and Profitability. Management Science, 51, 133–150 (2005)CrossRefGoogle Scholar
  67. 67.
    Ponsati, C., Sakovics, J.: Rubinstein Bargaining with Two-sided Outside Options. Econometric Theory, 11, 667–672 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  68. 68.
    Porteus, E: Responsibility Tokens in Supply Chain Management. Manufacturing, Service & Operations Management, 2, 203–219 (2000)CrossRefGoogle Scholar
  69. 69.
    Raju, J., Z.J. Zhang (2005) Channel Coordination in the Presence of a Dominant Retailer. Marketing Science, 24, pp. 254–262CrossRefGoogle Scholar
  70. 70.
    Rudi, N., Kapur, S., Pyke, D.F.: A Two-Location Inventory Model with Transshipment and Local Desicion Making. Management Science, 47, 1668–1680 (2001)CrossRefGoogle Scholar
  71. 71.
    Rapoport, A.: N-person Game Theory: Concepts and Applications. Dover Publications, New York (2001)zbMATHGoogle Scholar
  72. 72.
    Raghavan, T.E.S., Filar, J.A.: Algorithms for Stochastic Games—a Survey. ZOR - Methods and Models of Operations Research, 35, 437–472 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  73. 73.
    Robinson, L.: 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 (1993)CrossRefGoogle Scholar
  74. 74.
    Rubinstein, A.: Perfect Equilibrium in a Bargaining Model. Econometrica, 50, 155–162 (1982)CrossRefGoogle Scholar
  75. 75.
    Rudi, N., Netessine, S.: Centralized and Competitive Inventory Models with Demand Substitution. Operations Research, 51(2), 329–335 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  76. 76.
    Shapley, L.S.: A Value for n-Person Games. In: Kuhn, H.W., Tucker, W. (eds) Contributions to the Theory of Games. Vol. 2, Princeton University Press, Princeton, NJ (1953)Google Scholar
  77. 77.
    Shapley, L.S.: On Balanced Sets and Cores. Naval Research Logistics Quarterly, 14, 453–460 (1967)CrossRefGoogle Scholar
  78. 78.
    Slikker, M., Fransoo, J., Wouters, M.: Cooperation between Multiple News-Vendors with Transshipments. European Journal of Operational Research, 167, 370–380 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  79. 79.
    Spengler, J.J.: Vertical Restraints and Antitrust Policy. Journal of Political Economy, 58, 347–352 (1950)CrossRefGoogle Scholar
  80. 80.
    Ståhl, I.: Bargaining Theory. Stockholm School of Economics, Stockholm (1972)Google Scholar
  81. 81.
    Stuart, H.S. Jr.: Biform Analysis of Inventory Competition. Decision, Risk & Operations Working Papers Series, Columbia Business School (2004)Google Scholar
  82. 82.
    Tsay, A.: The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science, 45, 1339–1358 (1999)CrossRefGoogle Scholar
  83. 83.
    Tsay, A.A., Nahmias, S., Agrawal, N.: Modeling Supply Chain Contracts: A Review. In: Tayur, S., Ganeshan, R., Magazine, M. (eds) Quantitative Models for Supply Chain Management, International Series in Operations Research and Management Science, Vol. 17, Kluwer Academic Publishers, Norwell, MA, pp. 299–336 (1999)Google Scholar
  84. 84.
    Topkis, D.M.: Supermodularity and Complementarity. Princeton University Press, Princeton, NJ (1998)Google Scholar
  85. 85.
    van Damme, E.: Stability and Perfection of Nash Equilibria. Springer-Verlag, Berlin (1991)zbMATHGoogle Scholar
  86. 86.
    Van Mieghem, J., Dada, M.: Price Versus Production Postponement: Capacity and Competition. Management Science, 45, 1631– 1649 (1999)Google Scholar
  87. 87.
    Van Mieghem, J.: Coordinating Investment, Production and Subcontracting. Management Science, 45, 954–971 (1999)CrossRefGoogle Scholar
  88. 88.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ (1944)zbMATHGoogle Scholar
  89. 89.
    von Stackelberg: Marktform und Gleichgewicht. Stringer, Vienna (1934)Google Scholar
  90. 90.
    Wang, Q., Parlar, M.: Static Game Theory Models and Their Application in Management Science. European Journal of Operational Research, 42, 1–21 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  91. 91.
    Wang, H., Guo, M., Efstathiou, J.: A Game-Theoretical Cooperative Mechanism Design for a Two-Echelon Decentralized Supply Chain. European Journal of Operational Research, 157, 372–388 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  92. 92.
    Wang, Q., Parlar, M.: A Three-Person Game Theory Model Arising in Stochastic Inventory Control Theory. European Journal of Operational Research, 76, 83–97 (1994)zbMATHCrossRefGoogle Scholar
  93. 93.
    Weng, Z.K.: Channel Coordination and Quantity Discounts. Management Science, 41, 1509–1522 (1995)zbMATHCrossRefGoogle Scholar
  94. 94.
    Wu, S.D.: Supply Chain Intermediation: A Bargaining Theoretic Framework. In: Simchi-Levi, D., Wu, S.D., Shen, Z.M. (eds) Handbook of Quantitative. Supply Chain Analysis: Modeling in the E-Business Era, Kluwer Academic Publishers, New York, 67–115 (2004)Google Scholar
  95. 95.
    Yao, D.D.: S-Modular Game with Queuing Applications. Queuing System: Theory and Applications, 21, 449–475 (1995)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Altannar Chinchuluun
    • 1
  • Athanasia Karakitsiou
    • 2
  • Athanasia Mavrommati
    • 2
  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Production Engineering and ManagementTechnical University of CreteGreece

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