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Guaranteed Inertia Functions In Dynamical Games

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  • JEAN-PIERRE AUBIN

    ()
    (LASTRE (Laboratoire d'Applications des Systèmes Tychastiques Régulés), and Centre de Recherche Viabilité, Jeux, Contrôle, Université Paris-Dauphine, France)

  • PATRICK SAINT-PIERRE

    (LASTRE (Laboratoire d'Applications des Systèmes Tychastiques Régulés), and Centre de Recherche Viabilité, Jeux, Contrôle, Université Paris-Dauphine, France)

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    Abstract

    This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the controls regulating viable evolutions. For tychastic systems (parameterized systems where the parameters are tyches, disturbances, perturbations, etc.), the palicinesia of a tyche measure the worst norm over time of the velocities of the tyches. The palicinesia function is the largest palicinesia threshold c such that all evolutions with palicinesia smaller than or equal to c are viable. For dynamical games where one parameter is the control and the other one is a tyche (games against nature or robust control), we define the guaranteed inertia function associated with any initial state-control-tyche triple the best of the worst of the norms of the velocities of the controls and of the tyches and study their properties. Viability Characterizations and Hamilton-Jacobi equations of which these inertia and palicinesia functions are solutions are provided.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 08 (2006)
    Issue (Month): 02 ()
    Pages: 185-218

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    Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:02:p:185-218

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    Related research

    Keywords: Viability; dynamical games; inertia function; Tychastic systems; palicinesia;

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    Cited by:
    1. De Marco, Giuseppe & Romaniello, Maria, 2008. "Evolution of Coalition Structures under Uncertainty," MPRA Paper 14725, University Library of Munich, Germany, revised 16 Apr 2009.

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