Hyperbolicity of systems describing value functions in differential games which model duopoly problems
DOI:
https://doi.org/10.7494/dmms.2015.9.1.89Keywords:
duopoly models, semi-cooperative feedback strategies, Pareto optimality, hyperbolic partial differential equationsAbstract
Based on the Bressan and Shen approach ([2] or [7]), we present the extension of the class of non-zero sum dierential 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.References
Basar, T., Olsder, G.J., 1999. Dynamic Noncooperative Game Theory. SIAM.
Bressan, A., Shen, W., 2004. Semi-cooperative strategies for differential games. Int J Game Theory, 32, 561 - 593.
Chintagunta, P.K., Vilcassim, N.J., 1992. An empirical investigation of advertising strategies in a dynamic duopoly. Management Science, 38, 1230 - 1244.
Nash, J., 1950. The bargaining problem. Econometrica, 18, 155 - 162.
Nash, J., 1951. Non-cooperative games. Ann Math, 54, 286 - 295.
Serre, D., 2000. Systems of Conservation Laws I, II. Cambridge University Press.
Shen, W., 2009. Non-Cooperative and Semi-Cooperative Differential Games. Advances in Dynamic Games and Their Applications, Birkhauser Basel, 85 -106.
Wang, Q., Wu, Z., 2001. A duopolistic model of dynamic competitive advertising. European Journal of Operational Research, 128, 213 - 226.
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