Abstract
This study investigates implementation of a social choice function with complete information, where we impose various restrictions such as boundedness, permission of only small transfers, and uniqueness of iterative dominance in strict terms. We assume that the state is ex-post verifiable after the determination of allocation. We show that with three or more players, any social choice function is uniquely and exactly implementable in iterative dominance. Importantly, this study does not assume either expected utility or quasi-linearity, even if we utilize the stochastic method of mechanism design explored by Abreu and Matsushima (Econometrica 60:993–1008, 1992a; Econometrica 60:1439–1442, 1992b; J Econ Theory 64(1):1–19, 1994). We further show that even with incomplete information, and even with two players, any ex-post incentive compatible social choice function is uniquely and exactly implementable in iterative dominance.
Highlights
This study investigates unique and exact implementation of a social choice function under complete information
We show that any social choice function is uniquely, and exactly, implementable in iterative dominance, where we design a bounded mechanism, use only small transfers, and make no transfers on the equilibrium path
We show that even with incomplete information and even with two players, any ex-post incentive compatible social choice function is uniquely, and exactly, implementable in iterative dominance in the same manner as complete information with three or more players
Summary
This study investigates unique and exact implementation of a social choice function under complete information. We show that by making ex-post monetary transfers contingent on this verified information as well as their announcements, the central planner can design a mechanism to effectively penalize any detected liar, making all players willing to make their desirable announcements. We show that any social choice function is uniquely, and exactly, implementable in iterative dominance, where we design a bounded mechanism, use only small transfers, and make no transfers on the equilibrium path. In contrast to these works, this study focuses on another question on bounded rationality; can a player properly make the desirable choice at a step even if he (or she) is not the expected-utility maximizer? This study gives a positive answer to this question It is well known in the implementation literature that with no ex-post verifiability, Makin-monotonicity is a necessary condition for a social choice function to be implementable in Nash equilibrium (e.g., Maskin 1999).
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