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Characterization and Computation of Local Nash Equilibria in Continuous Games
Lillian Ratliff

Citation
Lillian Ratliff. "Characterization and Computation of Local Nash Equilibria in Continuous Games". Talk or presentation, 10, October, 2013.

Abstract
We present a derivative–based sufficient condition ensuring player strategies constitute local Nash equilibria in non–cooperative continuous games. Our results can be interpreted as generalizations of analogous second–order conditions for local optimality from nonlinear programming and optimal control theory. Drawing on this analogy, we propose an iterative steepest descent algorithm for numerical approximation of local Nash equilibria and provide a sufficient condition ensuring local convergence of the algorithm. We demonstrate our analytical and computational techniques by computing local Nash equilibria in games played on a finite–dimensional differentiable manifold or an infinite–dimensional Hilbert space.

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  • HTML
    Lillian Ratliff. <a
    href="http://www.truststc.org/pubs/924.html"
    ><i>Characterization and Computation of Local Nash
    Equilibria in Continuous Games</i></a>, Talk or
    presentation,  10, October, 2013.
  • Plain text
    Lillian Ratliff. "Characterization and Computation of
    Local Nash Equilibria in Continuous Games". Talk or
    presentation,  10, October, 2013.
  • BibTeX
    @presentation{Ratliff13_CharacterizationComputationOfLocalNashEquilibriaInContinuous,
        author = {Lillian Ratliff},
        title = {Characterization and Computation of Local Nash
                  Equilibria in Continuous Games},
        day = {10},
        month = {October},
        year = {2013},
        abstract = {We present a derivativeâbased sufficient
                  condition ensuring player strategies constitute
                  local Nash equilibria in nonâcooperative
                  continuous games. Our results can be interpreted
                  as generalizations of analogous secondâorder
                  conditions for local optimality from nonlinear
                  programming and optimal control theory. Drawing on
                  this analogy, we propose an iterative steepest
                  descent algorithm for numerical approximation of
                  local Nash equilibria and provide a sufficient
                  condition ensuring local convergence of the
                  algorithm. We demonstrate our analytical and
                  computational techniques by computing local Nash
                  equilibria in games played on a
                  finiteâdimensional differentiable manifold or an
                  infiniteâdimensional Hilbert space.},
        URL = {http://www.truststc.org/pubs/924.html}
    }
    

Posted by Carolyn Winter on 18 Nov 2013.
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