Computable models of static and dynamic spatial oligopoly

Amir H. Meimand, Terry Lee Friesz

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationHandbook of Regional Science
PublisherSpringer Berlin Heidelberg
Pages237-258
Number of pages22
ISBN (Electronic)9783642234309
ISBN (Print)9783642234293
DOIs
StatePublished - Jan 1 2014

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Oligopoly
Variational inequalities
Discretization
Control variable
Cournot-Nash
Competitors
Profit
Global optimization
Nash equilibrium
Dynamic games
Utility function
Market structure
Software
Nash solution
Network competition
Numerical methods
Dynamic oligopoly
Interaction
Economic fundamentals
Network model

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)
  • Business, Management and Accounting(all)

Cite this

Meimand, A. H., & Friesz, T. L. (2014). Computable models of static and dynamic spatial oligopoly. In Handbook of Regional Science (pp. 237-258). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-23430-9_105
Meimand, Amir H. ; Friesz, Terry Lee. / Computable models of static and dynamic spatial oligopoly. Handbook of Regional Science. Springer Berlin Heidelberg, 2014. pp. 237-258
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Meimand, AH & Friesz, TL 2014, Computable models of static and dynamic spatial oligopoly. in Handbook of Regional Science. Springer Berlin Heidelberg, pp. 237-258. https://doi.org/10.1007/978-3-642-23430-9_105

Computable models of static and dynamic spatial oligopoly. / Meimand, Amir H.; Friesz, Terry Lee.

Handbook of Regional Science. Springer Berlin Heidelberg, 2014. p. 237-258.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Meimand AH, Friesz TL. Computable models of static and dynamic spatial oligopoly. In Handbook of Regional Science. Springer Berlin Heidelberg. 2014. p. 237-258 https://doi.org/10.1007/978-3-642-23430-9_105