On generalized games in H -spaces

Paolo Cubiotti; Giorgio Nordo

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 175-180
  • ISSN: 0010-2628

Abstract

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We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in H -spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.

How to cite

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Cubiotti, Paolo, and Nordo, Giorgio. "On generalized games in $H$-spaces." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 175-180. <http://eudml.org/doc/248435>.

@article{Cubiotti1999,
abstract = {We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in $H$-spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.},
author = {Cubiotti, Paolo, Nordo, Giorgio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$H$-spaces; generalized games; Nash equilibria; $H$-convexity; open lower sections; fixed points; Nash equilibria; fixed points},
language = {eng},
number = {1},
pages = {175-180},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On generalized games in $H$-spaces},
url = {http://eudml.org/doc/248435},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Cubiotti, Paolo
AU - Nordo, Giorgio
TI - On generalized games in $H$-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 175
EP - 180
AB - We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in $H$-spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.
LA - eng
KW - $H$-spaces; generalized games; Nash equilibria; $H$-convexity; open lower sections; fixed points; Nash equilibria; fixed points
UR - http://eudml.org/doc/248435
ER -

References

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  6. Cubiotti P., Existence of solutions for lower semicontinuous quasi-equilibrium problems, Comput. Math. Applic. 30 (12) (1995), 11-22. (1995) Zbl0844.90094MR1360323
  7. Harker P.T., Generalized Nash games and quasi-variational inequalities, European J. Oper. Res. 54 (1991), 81-94. (1991) Zbl0754.90070
  8. Huang Y., Fixed point theorems with an application in generalized games, J. Math. Anal. Appl. 186 (1994), 634-642. (1994) Zbl0814.54029MR1293845
  9. Klein E., Thompson A.C., Theory of Correspondences, John Wiley and Sons, New York, 1984. Zbl0556.28012MR0752692
  10. Tian G., Zhou J., The Maximum theorem and the existence of Nash equilibria of (generalized) games without lower semicontinuities, J. Math. Anal. Appl. 166 (1992), 351-364. (1992) MR1160931

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