Essays On Microeconomics

Official URL: http://risc01.sabanciuniv.edu/record=b3422595

We consider Nash implementation under complete information with the additional feature that planners need obey fairness restrictions when designing mechanisms and shaping individuals’ unilateral deviation opportunities. An extreme form of such a notion of full implementation is anonymous implementation, which demands the following: First, any socially optimal alternative at any one of the given states is attainable via a Nash equilibrium (NE) at that state, which provides the same opportunity set for all individuals. Second, any such NE at any one of the states must be socially optimal at that state. We identify the necessary and (almost) sufficient conditions for the anonymous implementation of social choice correspondences. Further, we extend this concept to partitioned-anonymous implementation to allow for relaxed notions of fairness. First, agents are divided into equivalence classes (groups based on fairness considerations), delivering a partition over the set of individuals. Then, anonymity is required within each partition. This allows for a more flexible design while ensuring fairness within groups. We provide necessary and (almost) sufficient conditions for partitioned-anonymous implementation as well. Notwithstanding, we show that there are collective goals that are anonymously implementable but fail to be Nash implementable. Therefore, anonymity provides society with additional decentralizable social choice rules that are otherwise not Nash implementable. Unfortunately, anonymity imposes a heavy burden when implementing efficiency: The Pareto social choice correspondence is not anonymously implementable in the full domain.