The core

Setting aside the potential ambiguities in the definition of the characteristic function, if we have a theoretical description that appropriately summarizes a situation's strategic properties, then we should ask two questions of it. First, is there anything in the feasible set of utility outcomes, that is stable against all other possibilities, that offers itself as a compelling prediction? Second, if we can identify such outcomes, then what coalitions bring them about? These questions parallel our concerns in noncooperative theory: the definition and search for Nash equilibrium strategies and the outcome that prevails if players choose them. But now we focus on the actions of coalitions and on people as coalition members instead of atomistic decision makers. Game theory, or more precisely cooperative solution theory, has concentrated more on the issue of predicting outcomes, but the theory has taken some important steps in respect to predicting coalitions. This chapter, however, discusses a solution concept, the core, that is legitimately concerned solely with predicting outcomes.

If the characteristic function is appropriate to the circumstance, then the core provides a compelling prediction about outcomes. But not all games have a core, and we should understand what this means for politics. Because the core is a compelling hypothesis about cooperative games, we interpret its existence or nonexistence in a particular circumstance as an indicator of whether the final outcome is sensitive to the details of bargaining, to the coalition that ultimately forms, and to the idiosyncracies of the participants’ personalities, bargaining skills, and the like.