Common knowledge of rationality and market clearing in economies with asymmetric information
Consider an exchange economy with asymmetric information. What is the set of outcomes that are consistent with common knowledge of rationality and market clearing? To address this question we define an epistemic model for the economy that provides a complete description not only of the beliefs of each agent on the relationship between states of nature and prices but also of the whole system of interactive beliefs. The main result, theorem 1, provides a characterization of outcomes that are consistent with common knowledge of rationality and market clearing (henceforth, CKRMC outcomes) in terms of a solution notion - Ex - Post Rationalizability - that is defined directly in terms of the parameters that define the economy. We then apply theorem 1 to characterize the set of CKRMC outcomes in a general class of economies with two commodities. CKRMC manifests several intuitive properties that stand in contrast to the full revelation property of Rational Expectations Equilibrium: In particular, we obtain that for a robust class of economies: (1) there is a continuum of prices that are consistent with CKRMC in every state of nature, and hence these prices do not reveal the true state, (2) the range of CKRMC outcomes is monotonically decreasing as agents become more informed about the economic fundamentals, and (3) trade is consistent with common knowledge of rationality and market clearing even when there is common knowledge that there are no mutual gains from trade.