Beauty Contests and Iterated Expectations in Asset Markets

In a financial market where traders are risk averse and short lived and prices are noisy, asset prices today depend on the average expectation today of tomorrow’s price. Thus (iterating this relationship) the date 1 price equals the date 1 average expectation of the date 2 average expectation of the date 3 price. This will not, in general, equal the date 1 average expectation of the date 3 price. We show how this failure of the law of iterated expectations for average belief can help understand the role of higher-order beliefs in a fully rational asset pricing model. ‘‘ … professional investment may be likened to those newspaper com-petitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average pre-ferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not