Effectivity and Noncooperative Solution Concepts

Game theory analyzes the strategic aspects of situations of social interaction by representing them as mathematical structures. Any such structure should at least account for the participants’ powers and their preferences. The way powers and preferences are modelled makes a difference as to which strategic concepts are available for mathematical scrutiny. In strategic games the players’ powers are modelled as possible courses of action. This provides sufficient structure to analyze interactive situations by means of the noncooperative solution concepts, in particular Nash equilibrium. There are also different ways of representing the players’ powers. One of them being by means of effectivity sets, i.e., sets of outcomes in which a player can guarantee a game to end by choosing a particular course of action. One could favor this way of representing interactive situations as, indeed, it has been fashionable in recent formalisms, such as ATL, ATEL and coalition logic. This paper concerns the extent to which the notions available in strategic games are still applicable in case the players’ powers are represented in terms of their effectivity. We address this issue in particular for Nash equilibrium and a related solution concept, which we call outcome equilibrium.