Do humans rationally discount biased signals? Evidence from the Crawford-Sobel Game

In this paper I re-examine data from Cai and Wang's (2006) laboratory simulation of the Crawford-Sobel “strategic information transmission” game. Cai and Wang focus on the amount of information that senders in the game transmit to receivers, and largely ignore any effects of the bias of the information. More specific, Cai and Wang (and nearly all other researchers of whom I am aware) do not examine what I call the no-policy-bias implication of the Crawford-Sobel game. This implication is that the final policy that receivers choose, in expectation, should equal the policy that they would have chosen had the senders sent no signal. That is, the receivers should rationally discount any bias in the signals, and the senders should not be able systematically to fool the receivers. However, contrary to the theory of the Crawford-Sobel game, in practice, all versions of the Cai-Wang experiment produced a policy bias. Further, the bias was systematic—it was always in the direction that the senders preferred. Elsewhere (Groseclose, 2011) I estimate the media lambda, a number between zero and one that expresses the degree to which a signal sender can fool a receiver. The results of the Cai-Wang experiment produce a media lambda of approximately .32.