Implementation without expected utility: ex-post verifiability

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.