Partial ex-post verifiability and unique implementation of social choice functions
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Partial ex‑post verifiability and unique implementation of social choice functions Hitoshi Matsushima1 Received: 25 February 2019 / Accepted: 21 September 2020 © The Author(s) 2020
Abstract This study investigates the unique implementation of a social choice function in iterative dominance in the ex-post term. We assume partial ex-post verifiability; that is, after determining an allocation, the central planner can observe partial information about the state as verifiable. We demonstrate a condition of the state space, termed “full detection,” and show that with full detection, any social choice function is uniquely implementable even if the information that can be verified ex-post is very limited. To prove this, we construct a dynamic mechanism according to which each player announces his (or her) private signal, before the other players observe this signal, at an earlier stage, and each player also announces the state at a later stage. In this construction, we can impose several severe restrictions such as boundedness, permission of only tiny transfers off the equilibrium path, and no permission of transfers on the equilibrium path. This study does not assume either expected utility or quasi-linearity.
1 Introduction This study investigates the unique implementation of a social choice function (SCF). The equilibrium concept we adopt is an iteratively undominated strategy in the ex-post term, which is a very weak notion. Therefore, the uniqueness requirement is demanding. To achieve the allocation implied by a social choice function, which is contingent on the state, the unaware central planner must require informed players to reveal what they know about the state. Hence, the central planner must construct This is a drastic revision of a part of Matsushima (2017). This study was supported by a Grantin-aid for scientific research (KAKENHI 25285059) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the Japanese government. I am grateful to Takashi Kunimoto, Shunya Noda, Rene Saran, Satoru Takahashi, and Takashi Ui for their useful comments. All errors are mine. * Hitoshi Matsushima [email protected]‑tokyo.ac.jp 1
Department of Economics, University of Tokyo, Hongo, Bunkyo‑ku, Tokyo 113‑0033, Japan
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an appropriate mechanism that incentivizes each player to make the desirable (i.e., truthful) announcements as unique equilibrium behavior. This construction should be generally regarded as a difficult task. To overcome the difficulty, we assume partial ex-post verifiability, that is, after determining an allocation, the central planner can only observe partial information about the state. This observation is verifiable and contractible ex-post. Hence, to resolve the difficulty presented by this uniqueness issue, the central planner makes ex-post monetary transfers with these players. These transfers are contingent not only on players’ announcements, but also on the verifiable information. We t
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