MULTI-STAGE HIERARCHICAL GAMES: EXISTENCE AND STABILITY WHEN THE OPTIMAL RESPONSES ARE UNIQUE
Our main objects are two-person, multi-stage, Stackelberg games. We consider feedback solutions. Existence and variational stability of equilibria have been established under minimal assumptions when the optimal responses are unique.
Stackelberg games, Nash equilibrium, feedback solutions, repeated play, data perturbations.
Received: February 20, 2023; Accepted: March 27, 2023; Published: April 19, 2023
How to cite this article: Nunzia A. D’Auria, Multi-stage hierarchical games: existence and stability when the optimal responses are unique, Far East Journal of Applied Mathematics 116(2) (2023), 133-147. http://dx.doi.org/10.17654/0972096023008
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References:
[1] A. Bagchi, Stackelberg differential games in economic model, Lecture Notes in Control and Information Sciences, 64, Springer-Verlag, Berlin, 1984.[2] T. Basar and G. J. Olsder, Dynamic Noncooperative Games, Reprint of the Second 1995 Edition, SIAM Philadelphia, PA, 1999.[3] S. Flam, L. Mallozzi and J. Morgan, A new look on Stackelberg Cournot equilibria in oligopolistic markets, Economic Theory 20 (2002), 183-188.[4] J. Harsany, Games with incomplete information played by Bayesian players, Management Science 14 (1967), 159-182.[5] K. J. Lancaster, A new approach to consumer theory, Journal of Political Economy 74 (1966), 132-157.[6] P. Loridan and J. Morgan, A theoretical approximation scheme for Stackelberg problems, Journal of Optimization Theory and Applications 61 (1989), 95-110.[7] L. Mallozzi and J. Morgan, Existence of a feedback equilibrium for two-stage Stackelberg games, IEEE Transactions on Automatic Control 42 (1997), 1612-1614.[8] L. Mallozzi and R. Messalli, Multi-leader multi-follower model with aggregative uncertainty, Games 8(3) (2017), 1-14.[9] J. Moon and T. Başar, Discrete-time stochastic Stackelberg dynamic games with a large number of followers, 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, USA, 2016, pp. 3578-3583.[10] J. Morgan, Constrained well-posed two-level optimization problems, F. H. Clarke, V. F. Demyanov and F. Giannessi, eds., Non Smooth Optimization and Related Topics, Plenum Press, New York and London, 1989, pp. 307-325.[11] R. Myerson, Refinements of the Nash equilibrium concept, International Journal of Game Theory 7 (1978), 73-80.[12] K. Okuguchi and F. Szidarovszky, The Theory of Oligopoly with Multi-product Firms, Springer Verlag, Berlin, 1999.[13] H. Poppe, Compactness in General Function Spaces, VEB Deut. Verlag der Wissenschaften, Berlin, 1974.[14] C. G. Reid, The Kinked Demand Curve Analysis of Oligopoly, Edinburgh Univ. Press, 1981.[15] J. Roberts and H. Sonnenschein, On the existence of Cournot equilibrium without concave profit functions, Journal of Economic Theory 13 (1976), 112-117.[16] R. Selten, Reexamination of the perfectness for equilibrium points, International Journal of Game Theory 4 (1975), 25-55.[17] M. Shubik, Strategy and Market Structure, Wiley, New York, 1959.[18] K. Stankova and B. De Schutter, Stackelberg equilibria for discrete-time dynamic games - Part I: Deterministic games, Proceedings of the 2011 IEEE International Conference on Networking, Sensing and Control, Delft, The Netherlands, 2011, pp. 249-254.[19] E. van Damme, Stability and Perfection of Nash Equilibria, Springer-Verlag, 1987.[20] H. Von Stackelberg, Marktform und Gleichgewicht, Springer-Verlag, Vienna, 1934.