Asset prices and trading volume in a beauty contest

Speculators buy an asset hoping to sell it later to investors with higher private valuations. If agents are uncertain about the distribution of private valuations and about the beliefs of others about this distribution, a beauty contest with an infinite hierarchy of beliefs arises. Under Harsanyi's assumption of a common prior the infinite beliefs hierarchy is readily solved using Bayes' law. This paper shows that common knowledge of the "beliefs formation rule," mapping the private valuation of each agent into his first-order belief, also simplifies the beliefs hierarchy while allowing for disagreement among agents. We analyse the resulting speculation in a stylized asset market. Several statistics, computed only from readily observable quote, return and volume data, are evaluated in terms of their power to discriminate between genuine disagreement and the Harsanyian case. Only statistics that relate volume and volatility, or volume and changes in best offers, have the necessary discriminatory power.