Modeling cooperative decision situations: the deviation function form and the equilibrium concept

Rosenthal (J Econ Theory 5:88–101, 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 each proposed outcome. The present 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, we propose a new model, called deviation function form. The novelty is that, besides providing a detailed description of an outcome, the model captures new kinds of coalitional interactions that support the agreements proposed by deviating coalitions and that cannot be identified via the effectiveness form. Furthermore, it can be used to model the existent matching markets. Its formulation allows defining a new solution concept, which characterizes the cooperative equilibria and extends the stability concept of the existent matching models. The connection between the core and the cooperative equilibrium concepts is established.