Implementation by Codes of Rights

Implementation of a solution can be thought of as a way to design power distribution in a society such that for each admissible preference profile, the set of equilibrium outcomes coincides with the set of outcomes that the solution would select for it. By using the notion of a rights structure to formalize the idea of power distribution, Koray and Yildiz (2018) show that implementation (in core equilibria) by a right structure is equivalent to implementation via a rights structure in which only singleton coalitions have blocking powers - aka individual based rights structure. Since a natural way to design power distribution in a society is to design codes of rights, we formulate and fully characterize implementability by codes of rights as well as by codes of individual rights, and show that their insight do not extend to this notion of implementation. This result is robust and extends to alternative notions of core, such as that of externally stable core