MODELING COOPERATIVE DECISION SITUATIONS: THE DEVIATION FUNCTION FORM AND THE EQUILIBRIUM CONCEPT

Rosenthal (1972) points out that the coalitional function form may be insufficient to analyze some strategic interactions of the cooperative normal form. His solution consists in representing games in effectiveness form, which explicitly describes the set of possible outcomes that each coalition can enforce by a unilateral deviation from any proposed outcome. This paper detects some non-appropriateness of the effectiveness representation with respect to the stability of outcomes against coalitional deviations. In order to correct such inadequacies, it is proposed a new model, called deviation function form, which modifies Rosenthal’s setting by also modeling the coalition structure, in an appropriate way, and by incorporating new kinds of coalitional interactions, which support the agreements proposed by deviating coalitions. This modification propitiates that the concept of stability of the matching models, viewed as a cooperative equilibrium concept, be translated to any game in the deviation function form and be confronted with the traditional notion of core. Precise answers are given to the questions raised.