Ex-post implementation with social preferences

The current literature on mechanism design in models with social preferences discusses social-preference-robust mechanisms, i.e., mechanisms that are implementable in any environment with social preferences. The literature also discusses payoff-information-robust mechanisms, i.e., mechanisms that are implementable for any belief and higher-order beliefs of the agents about the payoff types of the other agents. In the present paper, I address the question of whether deterministic mechanisms that are robust in both of these dimensions exist. I consider environments where each agent holds private information about his personal payoff and about the existence and extent of his social preferences. In such environments, a mechanism is robust in both dimensions only if it is ex-post implementable, i.e., only if incentive compatibility holds for every realization of payoff signals and for every realization of social preferences. I show that ex-post implementation of deterministic mechanisms is impossible in such environments; i.e., deterministic mechanisms that are both social-preference-robust and payoff-information-robust do not exist.