How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object...

An entrepreneur contracts with a consultant, who is protected by limited liability, to supply information about the state of a project prior to investing in it. For a given level of investment, a good project succeeds with higher probability than a bad one. The entrepreneur makes an upfront...