Abstract
Existence and location of Stackelberg equilibria is studied for two players by using appropriate variational inequalities and fixed point arguments. Both compact and non-compact strategy sets are considered in Euclidean spaces; in the non-compact case, we apply arguments from the theory of (discrete and continuous) projective dynamical systems. Some examples are also presented.
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References
Amir R., Grilo I.: Stackelberg versus cournot equilibrium. Games Econ. Behav. 26, 1–21 (1999)
Cavazzuti E., Pappalardo M., Passacantando M.: Nash equilibria, variational inequalities, and dynamical systems. J. Optim. Theory Appl. 114(3), 491–506 (2002)
Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds.): Pareto Optimality, Game Theory and Equilibria, Springer Optimization and Its Applications, vol. 17. Springer, New York (2008)
Giannessi, F., Maugeri, A., Pardalos, P.M. (eds.): Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods, Nonconvex Optimization and its Applications, vol. 58. Kluwer, Dordrecht (2001)
Kristály A.: Location of nash equilibria: a riemannian geometrical approach. Proc. Am. Math. Soc. 138, 1803–1810 (2010)
Kristály, A., Rădulescu, V., Varga, Cs.: Variational principles in mathematical physics, geometry, and economics. Cambridge University Press, Encyclopedia of Mathematics and its Applications, No. 136, 2010
Moskovitz D., Dines L.L.: Convexity in a linear space with an inner product. Duke Math. J. 5, 520–534 (1939)
Migdalas, A., Pardalos, P.M., Värbrand, P. (eds.): Multilevel Optimization: Algorithms and Applications, Nonconvex Optimization and its Applications, vol. 20. Kluwer, Dordrecht (1998)
Novak A.J., Feichtinger G., Leitmann G.: A differential game related to terrorism: nash and stackelberg strategies. J. Optim. Theory Appl. 144(3), 533–555 (2010)
Pang J.-S., Fukushima M.: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. CMS 2, 21–56 (2005). doi:10.1007/s10287-004-0010-0
Stanford W.: Pure strategy nash equilibria and the probabilistic prospects of stackelberg players. Oper. Res. Lett. 38(2), 94–96 (2010)
Szulkin A.: Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 3(2), 77–109 (1986)
Xia Y.S., Wang J.: On the stability of globally projected dynamical systems. J. Optim. Theory Appl. 106(1), 129–150 (2000)
Zhang J., Qu B., Xiu N.: Some projection-like methods for the generalized nash equilibria. Comput. Optim. Appl. 45, 89–109 (2010)
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This work was supported by the grant PCCE-55/2008 “Sisteme diferentiale in analiza neliniara si aplicatii”.
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Nagy, S. Stackelberg equilibria via variational inequalities and projections. J Glob Optim 57, 821–828 (2013). https://doi.org/10.1007/s10898-012-9971-7
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DOI: https://doi.org/10.1007/s10898-012-9971-7