BENEFIT FUNCTION AND DUALITY IN FINITE NORMAL FORM GAMES

Walter Briec ()
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Walter Briec: University of Perpignan, 52 avenue Villeneuve, 66000 Perpignan, France

International Game Theory Review (IGTR), 2007, vol. 09, issue 03, 495-513

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.

Keywords: Mixed strategy; Nash equilibrium; finite normal form game; Luenberger benefit function; Σ-subdifferential; JEL: C72 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0219198907001564

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