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2014 | OriginalPaper | Buchkapitel

13. Computable Models of Static and Dynamic Spatial Oligopoly

verfasst von : Amir H. Meimand, Prof. Terry L. Friesz

Erschienen in: Handbook of Regional Science

Verlag: Springer Berlin Heidelberg

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Abstract

Oligopolies are a fundamental economic market structure in which the number of competing firms is sufficiently small so that the profit of each firm is dependent upon the interaction of the strategies of all firms. There are alternative behavioral assumptions one may employ in forming a model of spatial oligopoly. In this chapter, we study the classical oligopoly problem based on Cournot’s theory. The Cournot-Nash solution of oligopoly models assumes that firms choose their strategy simultaneously and each firm maximizes their utility function while assuming their competitor’s strategy is fixed. We begin this chapter with the basic definition of Nash equilibrium and the formulation of static spatial and network oligopoly models as variational inequality (VI) which can be solved by several numerical methods that exist in the literature. We then move on to dynamic oligopoly network models and show that the differential Nash game describing dynamic oligopolistic network competition may be articulated as a differential variational inequality (DVI) involving both control and state variables. Finite-dimensional time discretization is employed to approximate the model as a mathematical program which may be solved by the multi-start global optimization scheme found in the off-the-shelf software package GAMS when used in conjunction with the commercial solver MINOS. We also present a small-scale numerical example for a dynamic oligopolistic network.

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Literatur
Zurück zum Zitat Beckmann MJ, Puu T (1990) Spatial structures. Springer, Berlin/Heidelberg/New YorkCrossRef Beckmann MJ, Puu T (1990) Spatial structures. Springer, Berlin/Heidelberg/New YorkCrossRef
Zurück zum Zitat Brander JA, Zhang A (1993) Dynamic oligopoly behavior in the airline industry. Int J Ind Organ 11(3):407–435CrossRef Brander JA, Zhang A (1993) Dynamic oligopoly behavior in the airline industry. Int J Ind Organ 11(3):407–435CrossRef
Zurück zum Zitat Dafermos S, Nagurney A (1987) Oligopolistic and competitive behavior of spatially separated markets. Reg Sci Urban Econ 17(2):245–254CrossRef Dafermos S, Nagurney A (1987) Oligopolistic and competitive behavior of spatially separated markets. Reg Sci Urban Econ 17(2):245–254CrossRef
Zurück zum Zitat Friedman JW (1979) Oligopoly and the theory of games. North-Holland, New York Friedman JW (1979) Oligopoly and the theory of games. North-Holland, New York
Zurück zum Zitat Friesz TL (2010) Dynamic optimization and differential games. Springer, New YorkCrossRef Friesz TL (2010) Dynamic optimization and differential games. Springer, New YorkCrossRef
Zurück zum Zitat Friesz TL (1993) A spatial computable general equilibrium model. In: Proceedings of the workshop on transportation and computable general equilibrium models, Venice, 19–21 May 1993 Friesz TL (1993) A spatial computable general equilibrium model. In: Proceedings of the workshop on transportation and computable general equilibrium models, Venice, 19–21 May 1993
Zurück zum Zitat Friesz TL, Rigdon MA, Mookherjee R (2006) Differential variational inequalities and shipper dynamic oligopolistic network competition. Transp Res Pt B 40(6):480–503CrossRef Friesz TL, Rigdon MA, Mookherjee R (2006) Differential variational inequalities and shipper dynamic oligopolistic network competition. Transp Res Pt B 40(6):480–503CrossRef
Zurück zum Zitat Friesz TL, Harker PT (1984) Multicriteria spatial price equilibrium network design: theory and computational results. Transp Res Pt B 17(5):411–426CrossRef Friesz TL, Harker PT (1984) Multicriteria spatial price equilibrium network design: theory and computational results. Transp Res Pt B 17(5):411–426CrossRef
Zurück zum Zitat Greenhut M, Lane WJ (1989) Theory of oligopolistic competition. Manch Sch 57(3):248–261CrossRef Greenhut M, Lane WJ (1989) Theory of oligopolistic competition. Manch Sch 57(3):248–261CrossRef
Zurück zum Zitat Greenhut M, Norman G, Hung CS (1987) The economics of imperfect competition: a spatial approach. Cambridge University Press, Cambridge, UK Greenhut M, Norman G, Hung CS (1987) The economics of imperfect competition: a spatial approach. Cambridge University Press, Cambridge, UK
Zurück zum Zitat Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12(1):29–35CrossRef Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12(1):29–35CrossRef
Zurück zum Zitat Harker PT (1986) Alternative models of spatial competition. Oper Res 34(13):410–425CrossRef Harker PT (1986) Alternative models of spatial competition. Oper Res 34(13):410–425CrossRef
Zurück zum Zitat Harker PT (1984) Variational inequality approach for the determination of oligopolistic market equilibrium. Math Program 30(1):105–111CrossRef Harker PT (1984) Variational inequality approach for the determination of oligopolistic market equilibrium. Math Program 30(1):105–111CrossRef
Zurück zum Zitat Hashimoto H (1985) A spatial Nash equilibrium model. In: Harker PT (ed) Spatial price equilibria: advances in theory, computation, and application. Springer, Berlin/Heidelberg/New York, pp 20–41CrossRef Hashimoto H (1985) A spatial Nash equilibrium model. In: Harker PT (ed) Spatial price equilibria: advances in theory, computation, and application. Springer, Berlin/Heidelberg/New York, pp 20–41CrossRef
Zurück zum Zitat Henderson JM, Quandt RE (1980) Microeconomic theory: a mathematical approach, 3rd edn. McGraw-Hill, New York Henderson JM, Quandt RE (1980) Microeconomic theory: a mathematical approach, 3rd edn. McGraw-Hill, New York
Zurück zum Zitat Matsushima N, Matsumura T (2003) Mixed oligopoly and spatial agglomeration. Can J Econ 36(1):62–87CrossRef Matsushima N, Matsumura T (2003) Mixed oligopoly and spatial agglomeration. Can J Econ 36(1):62–87CrossRef
Zurück zum Zitat Markovich S (2008) Snowball: a dynamic oligopoly model with indirect network effects. J Econ Dyn Control 32(3):909–938CrossRef Markovich S (2008) Snowball: a dynamic oligopoly model with indirect network effects. J Econ Dyn Control 32(3):909–938CrossRef
Zurück zum Zitat Murphy FH, Sherali HD, Soyster AL (1982) A mathematical programming approach for deterministic oligopolistic market equilibriums. Math Program 24(1):92–106CrossRef Murphy FH, Sherali HD, Soyster AL (1982) A mathematical programming approach for deterministic oligopolistic market equilibriums. Math Program 24(1):92–106CrossRef
Zurück zum Zitat Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transp Res Pt E 38(5):281–303CrossRef Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transp Res Pt E 38(5):281–303CrossRef
Zurück zum Zitat Nagurney A (1999) Network economics: a variational inequality approach, Revised 2nd edn. Kluwer, BostonCrossRef Nagurney A (1999) Network economics: a variational inequality approach, Revised 2nd edn. Kluwer, BostonCrossRef
Zurück zum Zitat Nagurney A, Dupuis P, Zhang D (1994) A dynamical systems approach for network oligopolies and variational inequalities. Ann Oper Res 28(3):263–293 Nagurney A, Dupuis P, Zhang D (1994) A dynamical systems approach for network oligopolies and variational inequalities. Ann Oper Res 28(3):263–293
Zurück zum Zitat Nash J (1950) Equilibrium points in n-person games. Proceed Nat Aca Sci 36(1):48–49CrossRef Nash J (1950) Equilibrium points in n-person games. Proceed Nat Aca Sci 36(1):48–49CrossRef
Zurück zum Zitat Novshek W (1980) Equilibrium in Simple Spatial (or differentiated product) Models. Journal of Economic Theory 22(2):313–326CrossRef Novshek W (1980) Equilibrium in Simple Spatial (or differentiated product) Models. Journal of Economic Theory 22(2):313–326CrossRef
Zurück zum Zitat Raa T (1984) The distribution approach to spatial economics. J Reg Sci 24(1):105–117CrossRef Raa T (1984) The distribution approach to spatial economics. J Reg Sci 24(1):105–117CrossRef
Zurück zum Zitat Rovinskey RB, Shoemaker CA, Todd MJ (1980) Determining optimal use of resources among regional producers under differing levels of cooperation. Oper Res 28(4):859–866CrossRef Rovinskey RB, Shoemaker CA, Todd MJ (1980) Determining optimal use of resources among regional producers under differing levels of cooperation. Oper Res 28(4):859–866CrossRef
Zurück zum Zitat Tobin RT, Friesz TL (1983) Formulating and solving the spatial price equilibrium problem with transshipment in terms of arc variables. J Reg Sci 23(2):187–198CrossRef Tobin RT, Friesz TL (1983) Formulating and solving the spatial price equilibrium problem with transshipment in terms of arc variables. J Reg Sci 23(2):187–198CrossRef
Zurück zum Zitat Wie BW, Tobin LT (1997) A dynamic spatial Cournot-Nash equilibrium model and an algorithm. Comput Econ 10(1):15–45CrossRef Wie BW, Tobin LT (1997) A dynamic spatial Cournot-Nash equilibrium model and an algorithm. Comput Econ 10(1):15–45CrossRef
Metadaten
Titel
Computable Models of Static and Dynamic Spatial Oligopoly
verfasst von
Amir H. Meimand
Prof. Terry L. Friesz
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-23430-9_105