A novel characterization of nash-implementable social choice rules via neutrality

Abstract

In this thesis, we study Nash implementability of social choice rules in relation with the neutrality notion. Several works in the literature provide a characterization of Nash-implementable social choice rules. However, they do not explicitly show the degree of neutrality property in the Nash equilibrium concept which is also existing in Nash-implementable rules. In this study, we define a weak version of the neutrality condition critical neutrality which is associated with the critical domain of a social choice rule. The critical neutrality notion when conjoined with Maskin monotonicity turns out to be equivalent to Nash implementability. Moreover, we propose an algorithm to obtain a maximal domain of preference profiles on which a specified social choice rule is Nash-implementable, by utilizing critical neutrality as a tool. The main result of the thesis is in support of the view that implementability on the full domain of preference profiles is highly related with implementability on the critical domain in Nash equilibrium and possibly, in other solution concepts.