Rationalizable implementation in finite mechanisms

We prove that the Maskin monotonicity⁎ condition (proposed by Bergemann et al. (2011)) fully characterizes exact rationalizable implementation in an environment with lotteries and transfers. Different from previous papers, our approach possesses many appealing features simultaneously, e.g., finite mechanisms with no integer game or modulo game are used; no transfers are made in any rationalizable profile; the message space is small; the implementation is robust to information perturbations in the sense of Oury and Tercieux (2012).