Preliminary Structure of Information Partitions

概要

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This paper provides a formal model to construct players' information partitions which are common knowledge between them. The model clarifies Aumann's claim to the notions of the state of the world and of a player's inability to distinguish the states. In this model, the world consists of (1) the physical facts and (2) the players' observation devices to observe those facts and each other's observation device. A state of the world is defined as a specification of the physical facts in the world and the type of each player's observation device. The indistinguishability of the states for a specific player is defined based on the identity of the recognition of the physical facts and of the other player's observation device. The information partitions are now derived form each player's inability to distinguish the states. As an application, we consider the asymmetric information partitions, i.e., the information partitions one of which is a refinement of the other. It is shown that such relation is impossible for the entire state space. We obtain a necessary and sufficient condition for that relation to be satisfied in the restricted state space.
静岡県立大学の論文