One Truth and a Thousand Lies: Focal Points in Mechanism Design

Truthtelling is often viewed as focal in direct mechanisms. We introduce two new notions of robust implementation based on the premise that society may be composed of "primitive'' agents who, whenever confronted with a strategy profile, anchor to truthtelling and make a limited number of comparisons. Instead of comparing all possible alternative strategies as they would at a Nash equilibrium, primitive agents only make comparisons with truthtelling. We impose a notion of robustness of implementation when society may contain from primitive to sophisticated agents (who then play à la Nash). We call these (group) resilient implementation. We compare them to well-known conditions that have appeared in the mechanism design literature. Resilient implementation is equivalent to secure implementation, while its group version is linked to a coalitional extension of secure implementation. In contrast to resilient implementation, we show that the latter delivers positive results in many domains and models of interest that we discuss. Moving away from the implementation approach, we close with some results when truth-reversion is seen as a property imposed directly on decision rules. Our results suggest that some strategy-proof rules are expected to work better than others in practical applications.