This thesis studies three issues in the field of implementation theory. In the first chapter, I examine the implementation of social choice rules under strong Nash equilibrium, when agents do not only care about the final outcomes, but also have a small intrinsic preference for honesty. Specifically, an agent is partially honest if she breaks ties in favour of a truthful strategy, when she faces indifference between outcomes. I present sufficient conditions for implementation in such cases and provide applications in matching and bargaining environments.
In the second chapter, I 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, I 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). I characterize the social choice rules that are implementable in the first case, while in the second case I
provide sufficient conditions for implementation. My results outline the difficulties of implementation in decentralized environments. As applications, I include some possibility results. First I prove the implementability of a weaker version of the stable rule in a constrained matching environment with partners and projects and second, I prove the implementability of the weak Pareto rule in a multi-issue environment with lexicographic preferences.
In the third chapter, I extend the positive results obtained in Dutta and Sen (2012) to the framework of rights structures. I show that the well-known unanimity condition is suffcient for implementation in such an environment when there is at least one partially honest agent
