Rationalizable implementation in finite mechanisms

We prove that the Maskin monotonicity condition (by Bergemann, Morris, and Tercieux (2011)) fully characterizes exact rationalizable implementation in an environ-ment with lotteries and transfers. Different from previous papers, our approach possesses many appealing features simultaneously, e.g., infinite mechanisms with no integer game or modulo game are used; no transfer is imposed on any rationalizable profile;the message space is small; the implementation is robust to information perturbationsand continuous in the sense of Oury and Tercieux (2012).