Non-Partitional Information on Dynamic State Spaces and the Possibility of Speculation

Abstract

We describe an environment in which the development of the world over time is an object of uncertainty for the individual. In this environment, a natural representation of information is in terms of non-partitional structures. However, not all non-partitional information can be justified in this way. We identify a set of conditions which are necessary and jointly sufficient for such a representation--namely, that the individual's information be such that (1) whatever is known is true, (2) whatever is known is known to be known, and (3) that information be nested. Moreover, these three conditions are precisely those identified in a paper by Gaenakoplos as precluding speculative trade in games iwth generalized information. Thus our discussion provides an alternative perspective on the issue of speculation.