We study a mechanism design problem where the outside option is a default game. Players can reject the mechanism and play the default game non-cooperatively. We show that some allocation rules are implemented only when some players reject. Rejection is useful since it enables a player to signal private information. We establish a condition under which rejection is not required for implementation.
CELIK, G. and PETERS, M. (2011). Equilibrium Rejection of a Mechanism. Games and Economic Behavior, 73(2), pp. 375-387.