We study an adverse selection problem, where an agent is able to understate his productivity, but not allowed to overstate it. The solution to this problem is generally different than the solution to the standard problem, where no restriction is made on the statements of the agent. We identify a sufficient condition, that does not depend on the distribution of types, under which these two solutions coincide.
CELIK, G. (2006). Mechanism Design with Weaker Incentive Compatibility Constraints. Games and Economic Behavior, 56(1), pp. 37-44.