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Benefit Function And Duality In Finite Normal Form Games

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  • WALTER BRIEC

    ()
    (University of Perpignan, 52 avenue Villeneuve, 66000 Perpignan, France)

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    Abstract

    Luenberger (1992, 1994) introduced a function he terms the benefit function, that converts preferences into a numerical function and has some cardinal meaning. In this paper, we show that the benefit function enjoys many interesting properties in a game theory context. We point out that the benefit function can be adapted to compare the mixed profiles of a game. Along this line, inspired from the Luenberger's approach, we propose a dual framework and establish a characterization of Nash equilibriums in terms of the benefit function. Moreover, some criterions are provided to identify the efficient mixed strategies of a game (which differ from the Pareto efficient strategies). Finally, we go a bit further proposing some issue in comparing profiles and equilibriums of a game. This we do using the so-called Σ-subdifferential of the benefit function.

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    Bibliographic Info

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

    Volume (Year): 09 (2007)
    Issue (Month): 03 ()
    Pages: 495-513

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    Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:03:p:495-513

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    Related research

    Keywords: Mixed strategy; Nash equilibrium; finite normal form game; Luenberger benefit function; Σ-subdifferential; JEL: C72;

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