Contextually Private Mechanisms

Consider a mechanism designer who employs a dynamic protocol to implement a choice rule. A protocol violates the contextual privacy of an agent if the designer learns more of the agent's private information than is necessary for computing the outcome. Our first main result is a characterization of choice rules that can be implemented without producing any contextual privacy violations. We apply this result to show that many commonly studied and employed choice rules violate some agent's contextual privacy – the first-price auction and serial dictatorship rules are notable exceptions that can avoid violations altogether. Our second main result is a representation theorem for protocols that are contextual privacy equivalent. We use this result to derive a novel protocol for the second-price auction choice rule, the ascending-join protocol, which is more contextually private than the widespread ascending or English protocol.