We consider a bilateral trade model in which both players have a finite number of possible valuations. The sellers valuation and the buyers valuation for the object are private information, but the independent beliefs about these valuations are common knowledge. In this setting, we provide a characterization of the set of interim individually rational-implementable trading rules, analogous to the result of Myerson and Satterthwaite 1983. Thereafter, we derive necessary conditions for incentive compatible and ex post individually rational direct mechanisms. For the special class of corner mechanisms with discrete uniform beliefs, we characterize the set of ex post individually rational-implementable trading rules. In this context it is also shown that ex post efficiency can only be achieved if the number of different valuations is small. The maximal number of different valuations for which efficiency is still possible depends on the prior probability distribution of valuations.
