Sequential Preference Revelation in Incomplete Information Settings

Strategy-proof allocation rules incentivize truthfulness in simultaneous move games, but real world mechanisms sometimes elicit preferences sequentially. Surprisingly, even when the underlying rule is strategy-proof and non-bossy, sequential elicitation can yield equilibria where agents have a strict incentive to be untruthful. This occurs only under incomplete information, when an agent anticipates that truthful reporting would signal false private information about others' preferences. We provide conditions ruling out this phenomenon, guaranteeing all equilibrium outcomes to be welfare-equivalent to truthful ones.