Implementation with evidence

Abstract

We generalize the canonical problem ofNash implementation by allowing agents to voluntarily provide discriminatory signals, i.e., evidence. Evidence can either take the form of hard information or, more generally, have differential but non- prohibitive costs in different states. In such environments, social choice functions that are not Maskin-monotonic can be implemented. We formulate a more gen- eral property, evidence monotonicity, and show that this is a necessary condition for implementation. Evidence monotonicity is also sufficient for implementation in economic environments. In some settings, such as when agents have small preferences for honesty, any social choice function is evidence-monotonic. Addi- tional characterizations are obtained for hard evidence. We discuss the relation- ship between the implementation problem where evidence provision is voluntary and a hypothetical problem where evidence can be chosen by the planner as part ofan extended outcome space.