Abstract
We consider the Stackelberg well-posedness for hierarchical potential games and relate it to the Tikhonov well-posedness of the potential function as a maximum problem. We also make some considerations about the strong and weak Stackelberg approximate equilibria.
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References
Bagchi A., Stackelberg differential games in economic models, Lecture Notes in Control and Information Sciences, 64, Springer, Berlin, 1984.
Bard J., An efficient point algorithm for a linear two-stage optimization problem, Operations Research, 1983, 670–684.
Basar T. and Olsder G.J., Dynamic Noncooperative Game Theory, Academic Press, New York, 31, 1982.
Breton M., Aij A. and Haurie A., Sequential Stackelberg equilibria in twoperson games, Journal of Optimization Theory and Applications, 59, 1980, 71–97.
Cavazzuti E. and Morgan J., Well-posed saddle point problems, in Optimization, Theory and Algorithms (edJ._B. Hirriart-Urruty, W. Oettli and J. Stoer, (eds.), Proc. Conf. Confolant/France 1981, 1983, 61–76.
Chen C.I. and Cruz J.B., Stackelberg solution for two-person games with biased information patterns, IEEE Transaction on Automatic Control, 17, 1972, 791–798.
Dempe S., On an algorithm solving two-level programming problems with nonunique lower level solutions, Comp. Opti. Appl., 6, 1996, 227–249.
Dontchev A. and Zolezzi T., Well-posed optimization problems, Lecture Notes in Mathematics, 1543, Springer, Berlin, 1993.
Flam S., Mallozzi L. and Morgan J., A new look on Stackelberg Cournot equilibria in oligopolistic markets, Economic Theory, 20, 2002, 183–188.
Leitmann G., On generalized Stackelberg strategies, Journal of Optimization Theory and Applications, 26, 1978, 637–643.
Lignola M.B. and Morgan J., Topological existence and stability for Stackelberg problem. Journal of Optimization Theory and Applications, 84, 1997, 145–169.
Lignola M.B. and Morgan J., Stability for regularized bilevel programming problems, Journal of Optimization Theory and Applications, 93, 1997, 575–596.
Lignola M.B. and Morgan J., Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution, Journal of Global Optimization, 6, 2000, 57–67.
Loridan P. and Morgan J., New results on approximate solutions in two-level optimization, Optimization, 20, 1989, 819–836.
Loridan P. and Morgan J., Regularization for two-level optimization problems, Lecture Notes in Economic and Math. Systems, 382, 1992, 239–255.
Loridan P. and Morgan J., Weak via strong Stackelberg problem: new results, Journal of Global Optimization, 8, 1996, 263–287.
Mallozzi L. and Morgan J., Problema di Stackelberg con risposte pesate, Atti del XIX Convegno della Associazione per la Matematica Applicata alle Scienze Economiche e Sociali, 1995, 416–425.
Margiocco M., Patrone F. and Pusillo Chicco L., Anew approach toTikhonov well-posedness for Nash equilibria, Optimization, 40, 1997, 385–400.
Margiocco M., Patrone F. and Pusillo Chicco L., Metric characterizations of Tikhonov well-posedness in value, Journal of Optimization Theory and Applications, 100, n. 2, 1999, 377–387.
Margiocco M. and Pusillo L., Potential games and well-posedness properties, preprint 2005, submitted.
Monderer P. and Shapley L., Potential games, Games and Economic Behaviour, 14, 1996, 124–143.
Morgan J., Constrained well-posed two-level optimization problems, Nonsmooth Optimization and Related Topics, edited by F. H. Clarke, V. F. Dem’yanov and F. Giannessi, Plenum Press, NewYork, 1989, 307–325.
Morgan J. and Patrone F., Stackelberg problems: Subgame perfect equilibria via Tikhonov regularization, Advances in Dynamic Games: Applications to Economics, Management Science, Engineering, and Environmental Management (Haurie A., Muto S., Petrosjan L.A., and Raghavan T.E.S., eds), Bizkhauser, Boston, 2006, 209–221.
Patrone F., Well-posedness as an ordinal property, Rivista di Matematica pura ed applicata 1, 1987, 95–104.
Patrone F., Well posedness for Nash equilibria and related topics, Recent Developments in Well posed Variational Problems (Lucchetti R. and Revalski J., eds), Kluwer, Dordrecht, 1995, 211–227.
Simaan M. and Cruz J., On the Stackelberg strategy in nonzero-sum games, Journal of Optimization Theory and Applications, 11, 1973, 533–555.
Sheraly H.D., Soyster A.L. and Murphy F.H., Stackelberg-Nash-Cournot equilibria: characterizations and computations, Operations Research, 31, 1983, 253–276.
Von Stackelberg H., Marktform und Gleichgewitch, Springer, Vienna, 1934.
Voorneveld M., Potential games and interactive decisions with multiple criteria, CentER Dissertation Series, Tilburg University, 1999.
Voorneveld M., Tijs S. and Mallozzi L., Sequential production situations and potentials, Game Practice Book F. Patrone, I. Garcia Jurado, S. Tijs, (eds.), Kluwer Academic Publishers, Boston, 1999.
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Margiocco, M., Pusillo, L. (2007). StackelbergWell-Posedness and Hierarchical Potential Games. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_6
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DOI: https://doi.org/10.1007/978-0-8176-4553-3_6
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