Nash implementation with partially honest individuals

We investigate the problem of Nash implementation in the presence of “partially honest” individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome than that which obtains when lying. We show that when there are at least three individuals, all social choice correspondences satisfying No Veto Power can be implemented. If all individuals are partially honest and if the domain is separable, then all social choice functions can be implemented in strictly dominant strategies by a mechanism which does not use “integer/modulo games”. We also provide necessary and sufficient conditions for implementation in the two-person case, and describe some implications of these characterization conditions.