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2011 | 31 | 1 | 23-37
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Necessary conditions for linear noncooperative N-player delta differential games on time scales

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EN
Abstrakty
EN
We present necessary conditions for linear noncooperative N-player delta dynamic games on an arbitrary time scale. Necessary conditions for an open-loop Nash-equilibrium and for a memoryless perfect state Nash-equilibrium are proved.
Twórcy
  • Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
  • Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Bibliografia
  • [1] H. Abou-Kandil, G. Freiling, V. Ionescu and G. Jank, Matrix Riccati equations. In control and systems theory, Systems & Control: Foundations & Applications, Birkhäuser Verlag, Basel, 2003.
  • [2] Z. Bartosiewicz and E. Pawluszewicz, Realizations of linear control systems on times scales, Control and Cybernetics 35 (4) (2006), 769-786.
  • [3] M. Bohner and A. Peterson, Dynamic equations on time scales, An introduction with applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
  • [4] M. Bohner and A. Peterson, Advances in dynamic equations on time scales, Birkhäuser Boston, Inc., Boston, MA, 2003. doi: 10.1007/978-0-8176-8230-9
  • [5] R.A.C. Ferreira and D.F.M. Torres, Remarks on the calculus of variations on time scales, Int. J. Ecol. Econ. Stat. 9 F07 (2007), 65-73.
  • [6] R.A.C. Ferreira and D.F.M. Torres, Higher-order calculus of variations on time scales, Mathematical control theory and finance, (Springer, Berlin, 2008), 149-159.
  • [7] R.A.C. Ferreira and D.F.M. Torres, Necessary optimality conditions for the calculus of variations on time scales, arXiv:0704.0656.
  • [8] S. Hilger, Ein Ma{ßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universitäat Würzburg, 1988.
  • [9] S. Hilger, Differential and difference calculus- unified! Proceedings of the Second World Congress on Nonlinear Analysts, Part 5 (Athens, 1996). Nonlinear Analysis 30 (5) (1997), 2683-2694. doi: 10.1016/S0362-546X(96)00204-0
  • [10] G. Jank, Introduction to non-cooperative dynamical game theory, University of Aveiro, 2007 (personal notes).
  • [11] G. Leitmann, Cooperative and non-cooperative many players differential games, Course held at the Department of Automation and Information, July 1973. International Centre for Mechanical Sciences, Courses and Lectures No. 190, Wien - New York: Springer-Verlag, 1974.
  • [12] L.S. Pontryagin, V.G. Boltyanskij, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes, Translated from Russian by K.N. Trirogoff; edited by L.W. Neustadt, Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1126
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