Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes

We consider mechanism design in contexts in which agents exhibit bounded depth of reasoning (level k) instead of rational expectations. We use simple direct mechanisms, in which agents report only first-order beliefs. While level 0 agents are assumed to be truth tellers, level k agents best-respond to their belief that other agents have at most k - 1 levels of reasoning. We find that incentive compatibility is necessary for implementation in this framework, while its strict version alone is sufficient. Adding continuity to both directions, the same results are obtained for continuous implementation with respect to small modeling mistakes. We present examples to illustrate the permissiveness of our findings in contrast to earlier related results under the assumption of rational expectations