Regular Distributive Social Systems

I consider abstract social systems where individual owners make gifts according to their preferences on the distribution of wealth in the context of a noncooperative equilibrium. I define a condition of regularity and a condition of strong regularity of these social systems. I prove notably that: regularity is generic, and implies the local uniqueness of equilibrium and the uniqueness of status quo equilibrium; strong regularity is nongeneric, implies that an equilibrium exists for all initial distributions of wealth, whenever an equilibrium exists for one of them, and implies the connectedness of the range of the equilibrium correspondence. These properties have strong implications for distributive theory and policy, summarized in a general hypothesis of perfect substitutability of private and public transfers. The formulation and discussion of this hypothesis lead to a general assessment of the explanatory power of the theory.