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 impl
icit mapping from rejected outcomes into outcomes that are individually rat
ional. We call this voluntary implementation and show that the constrained
Walrasian correspondence is not voluntarily implementable. The second appro
ach 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 sh
ow that if players discount the future in any way, then the constrained Wal
rasian correspondence is stationarily implementable. Journal of Economic Li
terature (C) 2001 Academic Press.