Correlation, independence, and Bayesian incentives

Our goal is to describe the state of the art on Bayesian mechanisms when utility is transferable and only balanced transfers are admissible. New results will be proved along the way, but they will be integrated to the overall picture. We first study a condition on the information structure of the agents (condition B) which is necessary and sufficient to guarantee implementation of any decision rule. We prove constructively that condition B holds generically. We further analyze another condition (condition C), sufficient to guarantee implementation of any efficient decision rule and provide a simple interpretation. Also, we build a counterexample showing that condition C is not necessary to guarantee implementation of any efficient decision rule and then provide a necessary and sufficient condition. A counterexample is constructed to show that there does not always exist efficient Bayesian mechanisms, with three agents. Finally, we exhibit conditions on the information structures that guarantee unique implementation, and show that they hold generically.