Conditional Rights and Implementation

We study the issue of decentralization from the implementation perspective. In most cases of institution design, a social planner is forced to operate in a decentralized manner, by designing distinct institutions that deal with different issues or sectors, over which agents may have complementarities in their preferences. By utilizing the notion of a rights structure, we consider a two-sector environment and examine the possibilities that arise in implementation when the social planner can condition the rights structure of one sector to the one of the other. We distinguish two cases, one when a sector constitutes an institutional constraint (constrained conditional implementation), and one where both sectors can be objects of design (conditional implementation). We characterize the social choice rules that are implementable in the first case, while in the second case we provide sufficient conditions for implementation. Our results imply that it is in general more difficult to implement a rule in a decentralized environment. As applications of our characterization theorems, we include some possibility results. First we prove the implementability of a weaker version of the stable rule in a constrained matching environment with partners and projects and second, we prove the implementability of the weak Pareto rule in a multi-issue environment with lexicographic preferences.