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Author
Zwierzchowska Joanna (Nicolaus Copernicus University in Torun)
Title
Hyperbolicity of Systems Describing Value Functions in Differential Games which Model Duopoly Problems
Source
Decision Making in Manufacturing and Services, 2015, vol. 9, nr 1, s. 89-100, bibliogr. 8 poz.
Keyword
Teoria gier, Optimum Pareto
Game theory, Pareto optimality
Note
summ.
Abstract
Based on the Bressan and Shen approach (Bressan and Shen, 2004; Shen, 2009), we present an extension of the class of non-zero sum differential games for which value functions are described by a weakly hyperbolic Hamilton-Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly. (original abstract)
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Bibliography
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  1. Basar, T., Olsder, G.J., 1999. Dynamic Noncooperative Game Theory. SIAM.
  2. Bressan, A., Shen, W., 2004. Semi-cooperative strategies for differential games. International Journal of Game Theory, 32, pp. 561-593.
  3. Chintagunta, P.K., Vilcassim, N.J., 1992. An empirical investigation of advertising strategies in a dynamic duopoly. Management Science, 38, pp. 1230-1244.
  4. Nash, J., 1950. The bargaining problem. Econometrica, 18, pp. 155-162.
  5. Nash, J., 1951. Non-cooperative games. Ann Math, 54, pp. 286-295.
  6. Serre, D., 2000. Systems of Conservation Laws I, II. Cambridge University Press.
  7. Shen, W., 2009. Non-Cooperative and Semi-Cooperative Differential Games. Advances in Dynamic Games and Their Applications, Birkhauser Basel, pp. 85-106.
  8. Wang, Q., Wu, Z., 2001. A duopolistic model of dynamic competitive advertising. European Journal of Operational Research, 128, pp. 213-226.
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ISSN
2300-7087
Language
eng
URI / DOI
http://dx.doi.org/10.7494/dmms.2015.9.1.89
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