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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 648986, 8 pages
http://dx.doi.org/10.1155/2013/648986
Research Article

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.

Linked References

  1. L. Walras, Elements D'Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874.
  2. A. Wald, “On some systems of equations of mathematical economics,” Econometrica, vol. 19, pp. 368–403, 1951. View at MathSciNet
  3. K. J. Arrow and G. Debreu, “Existence of an equilibrium for a competitive economy,” Econometrica, vol. 22, pp. 265–290, 1954. View at MathSciNet
  4. D. Gale, “The law of supply and demand,” Mathematica Scandinavica, vol. 3, pp. 155–169, 1955. View at MathSciNet
  5. H. Nikaidō, Convex Structures and Economic Theory, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1968. View at MathSciNet
  6. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  7. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  8. 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. View at MathSciNet
  9. F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer Series in Operations Research and Financial Engineering, 2003.
  10. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  11. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  12. 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.
  13. A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  14. L. Scrimali, “A variational inequality formulation of the environmental pollution control problem,” Optimization Letters, vol. 4, no. 2, pp. 259–274, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  16. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  17. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  18. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  19. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  20. M. I. Kamenskii, V. V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space, W. deGruyter, Berlin, Germany, 2001.
  21. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  22. D. Chan and J. S. Pang, “The generalized quasivariational inequality problem,” Mathematics of Operations Research, vol. 7, no. 2, pp. 211–222, 1982. View at Publisher · View at Google Scholar · View at MathSciNet
  23. 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.