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Well Posedness and Optimization Problems

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 79))

Abstract

This contribution is in the field of Game Theory and Nash equilibria. The property of Tihkonov well posedness is analyzed in relation to other well posedeness properties which are ordinal, a very important property for games because it emphasizes the fact that players’ decisions are expressed by preferences and not by a special choice of utility function.

Relations between Twp of an exact potential game and Twp of potential function as maximum problem are considered too.

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References

  1. E. Cavazzuti, J. Morgan J, Well-Posed Saddle Point Problems in “Optimization, theory and algorithms” (J.B. Hirriart-Urruty, W. Oettli and J. Stoer eds.), Proc. Conf. Confolant/France 1981, (1983), 61–76.

    Google Scholar 

  2. A. Dontchev and T. Zolezzi, Well-posed Optimization Problems. Lecture Notes in Mathematics, 1543, Springer, Berlin, (1993).

    MATH  Google Scholar 

  3. V. Fragnelli, F. Patrone and A. Torre, The Nucleolus is Well Posed preprint 2003

    Google Scholar 

  4. M.B. Lignola and J. Morgan Well-posedness for Optimization Problems with Constraints Defined by Variational Inequalities having a Unique Solution J. Global Optimization 16 (2000),57–67.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Lucchetti, F. Patrone: Hadamard and Tyhonov Well-Posedness of Certain Class of Convex Functions, Journal of Mathematical Analysis and Applications 88, (1982), 204–215

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Lucchetti, F. Patrone, S. Tijs, Determinateness of two-person games. Bollettino U.M.I. 6: (1986), 907–924.

    MathSciNet  Google Scholar 

  7. M. Margiocco, F. Patrone, L. Pusillo Chicco: A New Approach to Tikhonov Well-Posedness for Nash Equilibria, Optimization 40, (1997), 385–400

    MATH  MathSciNet  Google Scholar 

  8. M. Margiocco, F. Patrone, and L. Pusillo Chicco: Metric Characterizations of Tikhonov Well-Posedness in Value, Journal of Optimization Theory Application, 100 n.2,(1999), 377–387.

    Article  MATH  MathSciNet  Google Scholar 

  9. Margiocco M., Patrone F., Pusillo Chicco L.: On Tikhonov well-posedness of concave games and Cournot oligopoly, Journal of Optimization Theory Application 112 (2002) 361–369

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Margiocco and L. Pusillo (ε,k) Equilibria and Well Posedness preprint (2003)

    Google Scholar 

  11. M. MARGIOCCO and L. PUSILLO: Value Bounded Approximations for Nash Equilibria preprint (2003)

    Google Scholar 

  12. M. Margiocco and L. Pusillo: Potential Games and Well-Posedness: Static and Dynamic Cases preprint (2004)

    Google Scholar 

  13. R.B. Myerson: Game Theory: Analysis of Conflict, Harvard University Press, Cambridge(MA) (1991)

    MATH  Google Scholar 

  14. P. Monderer, L. Shapley, Potential games, Games and Economic Behaviour 14, (1996), 124–143.

    Article  MATH  MathSciNet  Google Scholar 

  15. F. Patrone, Well-Posedness as an Ordinal Property. Rivista di Matematica pura ed applicata 1,(1987), 95–104.

    MATH  MathSciNet  Google Scholar 

  16. F. Patrone, Well-Posedness for Nash Equilibria and Related Topics in “Recent Developments in Well-Posed Variational Problems” Lucchetti R. and Revalski J. eds. Kluwer, Dordrecht, (1995).

    Google Scholar 

  17. F. Patrone and L. Pusillo Chicco, Antagonism for two person games: taxonomy and applications to Tihkonov well-posedness. preprint DMA (1995)

    Google Scholar 

  18. L. Pusillo Chicco: Approximate solutions and Tikhonov well-posedness for Nash equilibria, in “Equilibrium Problems: Nonsmooth Optimization and variational Inequality Models”, F. Giannessi, A. Maugeri and Panos M. Pardalos eds., Kluwer Academic Publishers (2001) 231–244

    Google Scholar 

  19. R.W. Rosenthal A class of games possessing pure strategy Nash equilibria International Journal of Game Theory 2 (1973)65–67

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Voorneveld, Potential Games and Interactive Decisions with Multiple Criteria. Center Dissertation Series. Tilburg University (1999).

    Google Scholar 

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Pusillo, L. (2005). Well Posedness and Optimization Problems. In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_51

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