Voluntary Implementation

We examine Nash implementation when individuals cannot be forced to accept the outcome of a mechanism. Two approaches are studied. The first approach is static where a state-contingent participation constraint defines an implicit mapping from rejected outcomes into outcomes that are individually rational. We call this voluntary implementation and show that the constrained Walrasian correspondence is not voluntarily implementable. The second approach is dynamic where a mechanism is replayed if the outcome at any stage is vetoed by one of the agents. We call this stationary implementation and show that if players discount the future in any way, then the constrained Walrasian correspondence is stationarily implementable.