Multistage information transmission with voluntary monetary transfer

We examine multistage information transmission with voluntary monetary transfer in the framework of Crawford and Sobel (1982). In our model, an informed expert can send messages to an uninformed decision maker more than once, and the uninformed decision maker can pay money to the informed expert voluntarily whenever she receives a message. Our results are that under some conditions (i) the decision maker can obtain more detailed information from the expert than that in the Crawford and Sobel model and (ii) there exists an equilibrium whose outcome Pareto dominates all the equilibrium outcomes in the Crawford and Sobel model. Moreover, we find the upper bound of the receiver's equilibrium payoff, and provide a sufficient condition for it to be approximated by the receiver’s payoff under a certain equilibrium.