An Example Where Imperfect Message Transmission Helps.
Myerson has an example on page 842 of this Handbook chapte
r with two possible states and three actions where communication fails if the messages always gets through, but helps some if they only get through half the time. Suppose the Sender knows the state of the world is A orB, with equal probability. The Receiver can choose X, Y, or Z. If the state is A, the Sender-Receiver payoffs are (2,3), (0,2), (-1,0). If the state is B, the Sender-Receiver payoffs are (1,0), (2,2), (0,3). If messages always get through, the Sender's message is irrelevant and the Receiver chooses Y, for a an expected payoff of 2 instead of 1.5 or 1.5. If the message is sent by a pigeon who gets shot down on the way with probability .5, then an equilibrium (not unique) is for the Sender to send the pigeon if the state is A but not if it is B and for the Receiver to choose X if the pigeon arrives and Y otherwise. Both players get higher expected payoffs as a result of using the "noisy" pigeon. See the link for more explanation.
Labels: Economics, game theory