Institutional enforceability

We introduce a new coalitional refinement of Nash equilibrium. An institution is defined to include: (i) a collection of active coalitions of players that can make joint deviations from any strategy profile; (ii) a partition of that collection, endowed with a priority order that determines which coalition is more important than another coalition; and (iii) a set-valued function that specifies which coalitions are informed about a joint deviation made by another coalition and can respond to that deviation by making a further deviation. The notion of institutional Nash equilibrium only considers joint deviations under the restrictions set by the institution under consideration. First, we reveal how our new equilibrium refinement is related to the existing coalitional refinements of Nash equilibrium. Second, after defining institutional enforceability as an availability of an equilibrium to be realized as a unique institutional Nash equilibrium for some institution, we characterize the conditions for an institutionally enforceable Nash equilibrium in two-player and three-player games.