Abstract

Painlevé-Kuratowski convergence results are obtained, under sufficient conditions of minimal character, for approximate Nash equilibria of two sequences of real valued functions. Moreover, an application to a hierarchical game is given

Author information

Contact details are reproduced from the original publication and may be historical.

Jacqueline Morgan

Dip. di Matematica, Università di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy

Roberto Raucci

Dip. di Scienze Economiche, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

References

  1. H. Attouch: Variational Convergences for Functions and Operators, Pitman, Boston, 1984.Google Scholar
  2. J. P. Aubin: Mathematical Methods of Game and Economy Theory, North Holland, Amsterdam, 1979.Google Scholar
  3. T. Basar, G. J. Olsder: Dynamic Noncoperative Game Theory, Academic Press, New York, 1982.Google Scholar
  4. E. Cavazzuti: Esistenza ed approssimazione di equilibri di Nash (1993), working paper.Google Scholar
  5. E. Cavazzuti, N. Pacchiarotti: Convergence of Nash equilibria, Bollettino U.M.I. 5-B (1986) 247-266.Google Scholar
  6. E. De Giorgi, T. Franzoni: Su un tipo di convergenza variazionale, Atti Accademia Nazionale Lincei, Scienze Matematiche, Fisiche e Naturali 58 (1975) 63-101.Google Scholar
  7. P. T. Harker, J. S. Pang: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications, Mathematical Programming 48 (1990) 161-220.https://doi.org/10.1007/BF01582255Google Scholar
  8. K Kuratowski: Topology, Academic Press, New York, 1966.Google Scholar
  9. G. Leitmann: On generalized Stackelberg strategies, Journal of Optimization Theory and Applications 26 (1978) 637-643.https://doi.org/10.1007/BF00933155Google Scholar
  10. M. B. Lignola: Ky Fan Inequalities and Nash equilibrium points with lack of semicontinuity and compactness, Journal of Optimization Theory and Applications 94(1) (1997) 137-145.https://doi.org/10.1023/A:1022611820107Google Scholar
  11. M. B. Lignola: Existence of Nash equilibrium and saddle points in infinite dimensional space, Optimization 43 (1997) 367-383.https://doi.org/10.1080/02331939808844394Google Scholar
  12. M. B. Lignola, J. Morgan: Convergence of marginal functions with dependent constraints, Optimization 23 (1992) 189-213.https://doi.org/10.1080/02331939208843758Google Scholar
  13. M. B. Lignola, J. Morgan: Semicontinuity of marginal functions in a sequential setting, Optimization 24 (1992) 241-252.https://doi.org/10.1080/02331939208843793Google Scholar
  14. M. B. Lignola, J. Morgan: Topological existence and stability for Stackelberg problems, Journal of Optimization Theory and Applications 84(1) (1995) 145-169.https://doi.org/10.1007/BF02191740Google Scholar
  15. P. Loridan, J. Morgan: New results on approximate solution in two level optimization, Optimization 20 (1989) 819-836.https://doi.org/10.1080/02331938908843503Google Scholar
  16. R. T. Rockafellar, R. Wets: Variational Analysis, Springer Verlag, Berlin, 1998.https://doi.org/10.1007/978-3-642-02431-3Google Scholar

Suggested citation

J. Morgan, R. Raucci. “New Convergence Results for Nash Equilibria.” Journal of Convex Analysis 6 (1999), No. 2, 377–385. https://doi.org/10.68381/jca06022

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.