Implementation in undominated strategies by bounded mechanisms: Some results on compromise alternatives

We consider an impossibility result in Börgers (1991), which says in a restricted environment with two players or three alternatives it is impossible to implement a social choice correspondence that is efficient, enforces compromises at a profile and is implementable in undominated strategies by a bounded mechanism. We extend and refine this result in many ways- we generalize the impossibility result for any number of players and alternatives when the compromises are enforced at a near-unanimous preference profile. We further show that the impossibility result in Börgers (1991) holds good if we replace efficiency of SCCs by neutrality. Also the impossibility result holds good for two agents and any number of alternatives when the SCC is unanimous and minimal. Interestingly, we get a possibility result when we relax the assumption of minimality.