Eliminating Redundancies in Partition Spaces

Redundancy in models of uncertainty is a non-trivial concept. We address this issue in the framework of partition spaces, introduced to game theory by Aumann (1976). In these models the uncertainty of agents is about a space of points, which are called states of the world. Each such state stands for a combination of physical, environmental parameters --- the state of nature, and possible mutual uncertainties of the agents over these parameters. These uncertainties are expressed by a partition each agent has over the states of the world: every partition member contains all those states the agent conceives as possible when one of them prevails.