Hyperbolicity of Systems Describing Value Functions in Differential Games which Model Duopoly Problems

• Autorzy: Zwierzchowska J.

Identyfikatory

DOI

10.7494/dmms.2015.9.1.89

• Konferencja: 10th Spain-Italy-Netherlands Meeting on Game Theory (SING10)
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

duopoly models; semi-cooperative feedback strategies; Pareto optimality; hyperbolic partial differential equations

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Decision Making in Manufacturing and Services
• Rocznik: 2015
• Tom: Vol. 9, no. 1
• Strony: 89--100
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Zwierzchowska J.

• Nicolaus Copernicus University in Torun, Faculty of Mathematics and Computer Sciences, Torun, Poland

Bibliografia

• 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.