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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 648986, 8 pages
Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities
1Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy
2Department of Mathematics and Computer Science, University of Messina, 98166 Messina, Italy
Received 3 March 2012; Revised 8 December 2012; Accepted 18 December 2012
Academic Editor: Sining Zheng
Copyright © 2013 I. Benedetti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. Walras, Elements D'Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874.
- A. Wald, “On some systems of equations of mathematical economics,” Econometrica, vol. 19, pp. 368–403, 1951.
- K. J. Arrow and G. Debreu, “Existence of an equilibrium for a competitive economy,” Econometrica, vol. 22, pp. 265–290, 1954.
- D. Gale, “The law of supply and demand,” Mathematica Scandinavica, vol. 3, pp. 155–169, 1955.
- H. Nikaidō, Convex Structures and Economic Theory, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1968.
- A. Barbagallo and M. G. Cojocaru, “Dynamic vaccination games and variational inequalities on time-dependent sets,” Journal of Biological Dynamics, vol. 4, no. 6, pp. 539–558, 2010.
- A. Barbagallo, P. Daniele, and A. Maugeri, “Variational formulation for a general dynamic financial equilibrium problem: balance law and liability formula,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 3, pp. 1104–1123, 2012.
- M. De Luca and A. Maugeri, “Quasi-variational inequalities and applications to equilibrium problems with elastic demand,” in Nonsmooth Optimization and Related Topics, F. M. Clarke, V. F. Demyanov, and F. Giannessi, Eds., vol. 43, pp. 61–77, Plenum, New York, NY, USA, 1989.
- F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer Series in Operations Research and Financial Engineering, 2003.
- S. Giuffrè, G. Idone, and S. Pia, “Some classes of projected dynamical systems in Banach spaces and variational inequalities,” Journal of Global Optimization, vol. 40, no. 1–3, pp. 119–128, 2008.
- G. Idone, A. Maugeri, and C. Vitanza, “Topics on variational analysis and applications to equilibrium problems,” Journal of Global Optimization, vol. 28, no. 3-4, pp. 339–346, 2004.
- A. Maugeri and C. Vitanza, “Time-dependent equilibrium problems,” in Pareto Optimality, Game Theory and Equilibria, A. Chinchuluun, A. Migdalas, P. Pardalos, and L. Pitsoulis, Eds., pp. 505–524, Springer, 2007.
- A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic, 1993.
- L. Scrimali, “A variational inequality formulation of the environmental pollution control problem,” Optimization Letters, vol. 4, no. 2, pp. 259–274, 2010.
- A. Jofré, R. T. Rockafellar, and R. J. B. Wets, “Variational inequalities and economic equilibrium,” Mathematics of Operations Research, vol. 32, no. 1, pp. 32–50, 2007.
- G. Anello, M. B. Donato, and M. Milasi, “A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption,” Journal of Global Optimization, vol. 48, no. 2, pp. 279–287, 2010.
- M. B. Donato, M. Milasi, and C. Vitanza, “An existence result of a quasi-variational inequality associated to an equilibrium problem,” Journal of Global Optimization, vol. 40, no. 1–3, pp. 87–97, 2008.
- M. B. Donato, M. Milasi, and C. Vitanza, “Quasi-variational approach of a competitive economic equilibrium problem with utility function: existence of equilibrium,” Mathematical Models & Methods in Applied Sciences, vol. 18, no. 3, pp. 351–367, 2008.
- A. Jofre, R. T. Rockafellar, and R. J.-B. Wets, “A variational inequality scheme for determining an economic equilibrium of classical or extended type,” in Variational Analysis and Applications, vol. 79, pp. 553–577, Springer, 2005.
- M. I. Kamenskii, V. V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space, W. deGruyter, Berlin, Germany, 2001.
- F. H. Clarke, Optimization and Nonsmooth Analysis, vol. 5 of Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 2nd edition, 1990.
- D. Chan and J. S. Pang, “The generalized quasivariational inequality problem,” Mathematics of Operations Research, vol. 7, no. 2, pp. 211–222, 1982.
- P. J. Lloyd, “The origins of the von Thunen-Mill-Pareto-Wicksell-Cobb-Douglas function,” History of Political Economy, vol. 33, pp. 1–19, 2001.