Ex-post implementation with social preferences
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Ex‑post implementation with social preferences Boaz Zik1 Received: 13 December 2018 / Accepted: 21 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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.
1 Introduction Models of mechanism design usually consider selfish agents, that is, agents whose utilities consist of their own personal payoffs. However, it is well established that in many economic environments subjects often have social preferences.1 In these environments, agents’ utilities depend not only on their own personal payoff but also on the payoffs of other agents in the society. In this paper, I study the problem of ex-post implementation of deterministic mechanisms in a simple model of
1 There is evidence in the experimental economics literature that subjects often have such “social” preferences. See Cooper et al. (2016) for a survey.
* Boaz Zik bzik@uni‑bonn.de 1
Institute for Microeconomics, University of Bonn, Bonn, Germany
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social preferences.2 I consider environments where each agent holds private information about his personal payoff from allocations and about the extent of his social preferences.3 In the first part of the paper, I investigate the implementation of decision rules that depend only on information about the agents’ personal payoffs. I find that the possibility of implementing such decision rules in environments with social preferences heavily depends on the solution concept that is used for the implementation. I first consider Bayesian implementation and reestablish the result of Bierbrauer and Netzer (2016) that for each decision rule that is implementable in the environment where agents are selfish, there exists a mechanism that implements it in a Bayes–Nash equilibrium in every environment with social preferences as well as in the environment where agents are selfish. I then consider ex-post implementation and show that the ex-pos
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