On noncooperative nonlinear differential games

Tomáš Roubíček

Kybernetika (1999)

  • Volume: 35, Issue: 4, page [487]-498
  • ISSN: 0023-5954

Abstract

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Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for the original game.

How to cite

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Roubíček, Tomáš. "On noncooperative nonlinear differential games." Kybernetika 35.4 (1999): [487]-498. <http://eudml.org/doc/33442>.

@article{Roubíček1999,
abstract = {Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for the original game.},
author = {Roubíček, Tomáš},
journal = {Kybernetika},
keywords = {noncooperative games; Nash equilibria; differential games; globally convex structure; noncooperative games; Nash equilibria; differential games; globally convex structure},
language = {eng},
number = {4},
pages = {[487]-498},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On noncooperative nonlinear differential games},
url = {http://eudml.org/doc/33442},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Roubíček, Tomáš
TI - On noncooperative nonlinear differential games
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 4
SP - [487]
EP - 498
AB - Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for the original game.
LA - eng
KW - noncooperative games; Nash equilibria; differential games; globally convex structure; noncooperative games; Nash equilibria; differential games; globally convex structure
UR - http://eudml.org/doc/33442
ER -

References

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