Skip to main content
SpringerLink
Log in

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

  • Chapter
Pareto Optimality, Game Theory And Equilibria

Part of the book series: Springer Optimization and Its Applications ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anand, K., Anupindi, R., Bassok, Y.: Strategic Inventories in Procurement Contracts. University of Pennsylvania, working paper (2002)

    Google Scholar 

  2. Anupindi, R., Bassok, Y.: Centralization of Stocks: Retailers vs. Manufacturer. Management Science, 45(2), 178–191 (1999)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  4. Avsar, Z.M., Baykal-Gürsoy, M.: Inventory Control under Substitutable Demand: A Stochastic Game Application. Naval Research Logistics, 49, 359–375 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  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. Bernstein, F., Marx, L.: Reservation Profit Levels and the Division of Supply Chain Profit. Duke University, working paper (2004)

    Google Scholar 

  7. Binmore, K.G., Runbinstein, A., Wolinsky, A.: The Nash Bargaining Solution in Economic Modelling, Rand Journal of Economics, 17, 176–188 (1986)

    Article  MathSciNet  Google Scholar 

  8. Binmore, K.G., Shaked, A., Sutton, J.: An Outside Option Experiment. Quarterly Journal of Economics, 104, 753–770 (1988)

    Article  MathSciNet  Google Scholar 

  9. Bondareva, O.: Some Applications of Linear Programming Methods to the Theory of Cooperative Games (in Russian). Problemi Kibernet, 10, 119–139 (1963)

    MathSciNet  Google Scholar 

  10. Brandenburger, A., Stuart, H.W.: Biform Games. Columbia University (revised August 2004), working paper (2003)

    Google Scholar 

  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. Cachon, G.P.: Stock Wars: Inventory Competition in a Two-Echelon Supply Chain. Operations Research, 49, 658–674 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  15. Cachon, G., Lariviere, M.A.: Supply Chain Coordination with Revenue Sharing Contracts: Strengths and Limitations. Management Science, 51, 30–44 (2005)

    Article  Google Scholar 

  16. Cachon, G.P., Lariviere, M.: Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance. Management Science, 45, pp. 1091–1108 (1999)

    Article  Google Scholar 

  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. 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. Cachon, G.P., Zipkin, P.H. Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain. Management Science, 45, 936–53 (1999)

    Article  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  22. Chen, F. Decentralized Supply Chains Subject to Information Delays. Management Science, 45, 1076–1090 (1999)

    Article  Google Scholar 

  23. Chod, J., Rudi, N.: Strategic Investments, Trading and Pricing under Forecast Updating. University of Rochester, working paper (2003)

    Google Scholar 

  24. Clark, A., Scarf, H.: Optimal Policies for a Multi-Echelon Inventory Problem. Management Science, 6, 475–490 (1960)

    Article  Google Scholar 

  25. Colman, A.M.: Game Theory and Its application. Routledge, New York (1999)

    Google Scholar 

  26. Dai, Y.: Game Theoretic Approach to Supply Chain Management. PhD Dissertation, North Carolina State University, Raleigh, NC (2003)

    Google Scholar 

  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. 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. Drezner, Z., Gurnani, H., Pasternack, B.A.: An EOQ Model with Substitutions Between Products. Journal of Operational Research Society, 46, 887–891 (1995)

    Article  MATH  Google Scholar 

  30. Emmons, H., Gilbert, S.: Returns Policies in Pricing and Inventory Decision for Cataloque Goods. Management Science, 44, 276–283 (1998)

    Article  MATH  Google Scholar 

  31. Eppen, G.D., Iyer, A.V.: Backup Agreements in Fashion Buying—the Value of Upstream Flexibility. Management Science, 43, 1469–1484 (1997)

    Article  MATH  Google Scholar 

  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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  35. Granot, D., Sosic, G.: A Three Stage Model for a Decentralized Distribution Systems of Retailers. Operations Research, 51(5), 771–784 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  36. Hartman, B., Dror, M.: Cost Allocation in Continuous Review Inventory Models. Naval Research Logistic Quarterly, 43, 549–561 (1996)

    Article  MATH  Google Scholar 

  37. Hartman, B., Dror, M., Shaked, M.: Cores of Inventory Centralization Games. Games and Economic Behavior, 31, 26–49 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  38. Heyman, D.P., Sobel, M.J.: Stochastic Models in Operations Research. Vol. II: Stochastic Optimization, McGraw-Hill, New York (1984)

    MATH  Google Scholar 

  39. Kalai, E., Smorodinsky, M.: Other Solutions to the Nash Bargaining Problem. Econometrica, 43, 513–518 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  40. Khouja, M.: The Single-Period (News-Vendor) Problem: Literature Review and Suggestions for Future Research. Omega, 27, 537–553 (1999)

    Article  Google Scholar 

  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. Kreps, M.D.: Game Theory and Economic Modelling. Oxford University Press, New York (2001)

    Google Scholar 

  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)

    Article  Google Scholar 

  44. Lee, H., Whang, J.: Decentralized Multi-Echelon Supply Chains: Incentives and Information. Management Science, 45, 633–640 (1999)

    Article  Google Scholar 

  45. Lee, H., Padmanabhan, P., Whang, S.: Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science, 43, 546–558 (1997)

    Article  MATH  Google Scholar 

  46. Lippman, S.A., McCardle, K.F.: The Competitive Newsboy. Operations Research, 45(1), 54–65 (1997)

    Article  MATH  Google Scholar 

  47. Lucas, W.F.: An Overview of the Mathematical Theory of Games. Management Science, 18(5), 3–19 (1972)

    Article  MathSciNet  Google Scholar 

  48. Mahajan, S., van Ryzin, G.J.: Inventory Competition Under Dynamic Consumer Choice. Operations Research, 49(5), 646–657 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  49. Müller, A., Scarsini, M., Shaked, M.: The Newsvendor Game Has a Non-Empty Core. Games and Economic Behavior, 38, 118–126 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  50. Muthoo, A.: On The Strategic Role of Outside Options in Bilateral Bargaining. Operations Research, 43, 292–297 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  51. Myerson, R.B.: Game Theory: Analysis of Conflicts. Harvard University Press, Boston (2002)

    Google Scholar 

  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. Napel, S.: Biletar Bargaining: Theory and Applications. Lecture Notes in Economics and Mathematical Systems, Vol. 518, Springer-Verlag, Heidelberg (2002)

    Google Scholar 

  54. Nash, J.F.: Equilibrium Points in n-Person Games. Proceedings of the National Academy of Sciences, 36, 48–49 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  55. Nash, J.F.: The Bargaining Problem. Econometrica, 18, 155–162 (1950)

    Article  MathSciNet  Google Scholar 

  56. Nash, J.F.: Non-Cooperative games. Annals of Mathematics, 54, 286–295 (1951)

    Article  MathSciNet  Google Scholar 

  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. Netessine, S., Rudi, N.: Centralized and Competitive Inventory Models with Demand Substitution. Operations Research, 53, 329–335 (2003)

    Article  MathSciNet  Google Scholar 

  59. Netessine, S., Rudi, N., Wang, Y.: Dynamic Inventory Competition and Customer Retention. working paper (2003)

    Google Scholar 

  60. Netessine, S., Shumsky, R.: Revenue Management Games: Horizontal and Vertical Competition. University of Pennsylvania, working paper (2001)

    Google Scholar 

  61. Osdorne, M.J., Rubinstein, A.: Bargaining and Markets. Academic Press, Inc., San Diego (1990)

    Google Scholar 

  62. Osdorne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge, Massachusetts (1994)

    Google Scholar 

  63. Parlar, M.: Game Theoretic Analysis of the Substitutable Product Inventory Problem with Random Demands. Naval Research Logistics, 35, 397–409 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  64. Pasternack, P.: Optimal Pricing and Return Policies for Perishable Commodities. Marketing Science, 4, 998–1010 (1985)

    Article  Google Scholar 

  65. Plambeck, L.E., Terry, A.: Implications of Renegotiation for Optimal Contract Flexibility and Investment. Working Paper, Stanford University (2004)

    Google Scholar 

  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)

    Article  Google Scholar 

  67. Ponsati, C., Sakovics, J.: Rubinstein Bargaining with Two-sided Outside Options. Econometric Theory, 11, 667–672 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  68. Porteus, E: Responsibility Tokens in Supply Chain Management. Manufacturing, Service & Operations Management, 2, 203–219 (2000)

    Article  Google Scholar 

  69. Raju, J., Z.J. Zhang (2005) Channel Coordination in the Presence of a Dominant Retailer. Marketing Science, 24, pp. 254–262

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  71. Rapoport, A.: N-person Game Theory: Concepts and Applications. Dover Publications, New York (2001)

    MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  74. Rubinstein, A.: Perfect Equilibrium in a Bargaining Model. Econometrica, 50, 155–162 (1982)

    Article  Google Scholar 

  75. Rudi, N., Netessine, S.: Centralized and Competitive Inventory Models with Demand Substitution. Operations Research, 51(2), 329–335 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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. Shapley, L.S.: On Balanced Sets and Cores. Naval Research Logistics Quarterly, 14, 453–460 (1967)

    Article  Google Scholar 

  78. Slikker, M., Fransoo, J., Wouters, M.: Cooperation between Multiple News-Vendors with Transshipments. European Journal of Operational Research, 167, 370–380 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  79. Spengler, J.J.: Vertical Restraints and Antitrust Policy. Journal of Political Economy, 58, 347–352 (1950)

    Article  Google Scholar 

  80. Ståhl, I.: Bargaining Theory. Stockholm School of Economics, Stockholm (1972)

    Google Scholar 

  81. Stuart, H.S. Jr.: Biform Analysis of Inventory Competition. Decision, Risk & Operations Working Papers Series, Columbia Business School (2004)

    Google Scholar 

  82. Tsay, A.: The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science, 45, 1339–1358 (1999)

    Article  Google Scholar 

  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. Topkis, D.M.: Supermodularity and Complementarity. Princeton University Press, Princeton, NJ (1998)

    Google Scholar 

  85. van Damme, E.: Stability and Perfection of Nash Equilibria. Springer-Verlag, Berlin (1991)

    MATH  Google Scholar 

  86. Van Mieghem, J., Dada, M.: Price Versus Production Postponement: Capacity and Competition. Management Science, 45, 1631– 1649 (1999)

    Google Scholar 

  87. Van Mieghem, J.: Coordinating Investment, Production and Subcontracting. Management Science, 45, 954–971 (1999)

    Article  Google Scholar 

  88. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ (1944)

    MATH  Google Scholar 

  89. von Stackelberg: Marktform und Gleichgewicht. Stringer, Vienna (1934)

    Google Scholar 

  90. Wang, Q., Parlar, M.: Static Game Theory Models and Their Application in Management Science. European Journal of Operational Research, 42, 1–21 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  93. Weng, Z.K.: Channel Coordination and Quantity Discounts. Management Science, 41, 1509–1522 (1995)

    Article  MATH  Google Scholar 

  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. Yao, D.D.: S-Modular Game with Queuing Applications. Queuing System: Theory and Applications, 21, 449–475 (1995)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Altannar Chinchuluun

  2. Department of Production Engineering and Management, Technical University of Crete, Greece

    Athanasia Karakitsiou & Athanasia Mavrommati

Authors
  1. Altannar Chinchuluun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Athanasia Karakitsiou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Athanasia Mavrommati
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos , Altannar Chinchuluun  & Panos M. Pardalos ,  & 

  2. Department of Production Engineering and Management, Technical University of Crete, 73100, Greece

    Athanasios Migdalas

  3. Department of Production Engineering and Management, Aristotle University of Thessaloniki, Greece

    Leonidas Pitsoulis

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Chinchuluun, A., Karakitsiou, A., Mavrommati, A. (2008). Game Theory Models and Their Applications in Inventory Management and Supply Chain. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_29

Download citation

Publish with us

Policies and ethics

Search

Navigation