The Nash Equilibrium in Multy-Product Inventory Model

Authors

  • Elena A. Lezhnina Saint Petersburg State University
  • Victor V. Zakharov Saint Petersburg State University

Abstract

In this paper game theory model of inventory control of a set of products is treated. We consider model of price competition. We assume that each retailer can use single-product and multi-product ordering . Demand for goods which are in stock is constant and uniformly distributed for the period of planning. Retailers are considered as players in a game with two-level decision making process. At the higher level optimal solutions of retailers about selling prices for the non-substituted goods forming Nash equilibrium are based on optimal inventory solution (order quantity or cycle duration) as a reaction to chosen prices of the players. We describe the price competition in context of modified model of Bertrand. Thus at the lower level of the game each player chooses internal strategy as an optimal reaction to competitive player’s strategies which are called external. Optimal internal strategies are represented in analytical form. Theorems about conditions for existences of the Nash equilibrium in the game of price competition are proved.

Keywords:

game theory, non-coalition game, Bertrand oligopoly, Nash equilibrium, logistics

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References

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

Harris, F. (1915). Operation and Cost. Factory Management Series. A.W. Shaw, Chicago, 48–52.

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

Nash, J. F. (1950). Equilibrium Points in n-Person Games. Proceedings of the National Academy of Sciences, 36, 48–59.

Dasgupta, P., Maskin, E. (1986). The Existence of Equilibrium in Discontinuous Economic Games. Review of Economics Studies, 53, 1–26.

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

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

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

Tirol, Jean (2000). The markets and the market power: The organization and industry theory. Translation from English by J. M. Donc, M. D. Facsirova, under edition A. S. Galperina and N. A. Zenkevich. SPb: Institute Economic school, in 2 Volumes. V.1. 328 p. V.2. 240 p.

Kukushkin, N. S., Morozov, V. V. (1984). The nonantagonistic Game Theory. M.: Moscow State University, 103 p.

Friedman, James (1983). Oligopoly Theory. Cambridge University Press, 260 p.

Bertrand, J. (1883).Theorie mathematique de la richesse sociale. Journal des Savants., 67, 499–508.

Cournot, A. A. (1883). Recherches sur les principes mathmatiques de la thorie des richesses. Paris, L. Hachette, 198 p.

Hax, A. C. and D. Candea (1984). Production and inventory management. Prentice-Hall. Englewood Cliffs, N.J., 135 p.

Haldey, G. and T. M. Whitin (1963). Analysis of inventory. Prentice-Hall, Englewood Cliffs, N.J.

Tersine, R. J. (1994). Principles of inventory and materials management. Elsevier North Holland, Amsterdam.

Cachon, G. P. (2003). Supply chain coordination with contracts. Handbook in Operations Research and Management Science: Supply Chain Management. Vol. 11, Elsevier B. V., Amsterdam, pp. 229–340.

Mansur Gasratov, Victor Zakharov (2011). Games and Inventory Management. In: Dynamic and Sustainability in International Logistics and Supply Chain Management. Cuvillier Verlag, Gottingen.

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Published

2022-08-09

How to Cite

A. Lezhnina, E., & V. Zakharov, V. (2022). The Nash Equilibrium in Multy-Product Inventory Model. Contributions to Game Theory and Management, 7. Retrieved from https://gametheory.spbu.ru/article/view/13602

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