BENEFIT FUNCTION AND DUALITY IN FINITE NORMAL FORM GAMES
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 Î£-subdifferential of the benefit function.
Mixed strategy, Nash equilibrium, finite normal form game, Luenberger benefit function, Î£-subdifferential, JEL: C72
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