2. The Permissible and the Forbidden

Following Richter and Rubinstein (2020), we analyze an equilibrium concept based upon social norms: the Y-equilibrium. A Y-equilibrium is a set of permissible alternatives and a profile of choices, one for each agent, such that:

(i) each agent's choice is optimal from among the permissible alternatives;

(ii) the profile of choices is feasible; and

(iii) the set of permissible alternatives is maximal in the sense that there is no superset of permissible alternatives from which a profile satisfying (i) and (ii) can be found.

By this definition, two forces make a permissible set unstable: The first modifies the permissible set in the case that the profile of (intended) choices is not feasible, while the second loosens restrictions on the permissible set as long as a new profile of optimal choices is feasible. We also consider a variant of this concept where we require that the permissible set is convex.

We study the Y-equilibria of a variety of examples and prove existence theorems, “welfare” theorems and a structure theorem when the set of alternatives is Euclidean.