We study a model of mechanism design in which the designer cannot force the players to use the mechanism. Instead they must voluntarily sign away their decision rights, and if they instead keep their decision rights they act on their own accord. We ask what social choice functions can be implemented uniquely in this setting. We show that when there is no incomplete information among the players our analysis differs little from that of the standard framework. However when there is incomplete information among the players we identify examples in which many social choice functions which are uniquely implementable in the standard framework cannot be implemented uniquely in ours. In some cases, simple mechanisms intended to produce desirable equilibria also produce equilibria with very bad welfare properties. We see this as a caution to applications of the standard analysis to the design of real markets.