An Impossibility Result for Virtual Implementation with Status Quo

In this paper, virtual implementation is restricted so that only a socially optimal outcome or some fixed outcome (a status quo) can be delivered on the equilibrium path. Under such a restriction, any unanimous and implementable social choice function is almost-dictatorial. That is, there is an agent who obtains the most preferable outcome as long as this outcome is better than status quo outcome for all agents. If the range of social choice functions is restricted to pure outcomes only, the result extends to outcomes that are worse than the status quo