Preferences, common knowledge and speculative trade

We study the proposition that if it is common knowledge that en allocation of assets is ex-ante pareto efficient, there is no further trade generated by new information. The key to this result is that the information partitions and other characteristics of the agents must be common knowledge and that contracts, or asset markets, must be complete. It does not depend on learning, on 'lemons' problems, nor on agreement regarding beliefs and the interpretation of information. The only requirement on preferences is state-additivity; in particular, traders need not be risk-averse. We also prove the converse result that "no-trade results" imply that traders' preferences can be represented by state-additive utility functions. We analyze why examples of other widely studied preferences (e.g., Schmeidler (1989)) allow "speculative" trade.

Two ways to common knowledge

It is not clear what a system for evidence-based common knowledge should look like if common knowledge is treated as a greatest fixed point. This paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence-based common knowledge. As an alternative, we study two different deductive systems for the logic of common knowledge. The first system makes use of an induction axiom whereas the second one is based on co-inductive proof theory. We show the soundness and completeness for both systems.