Interactive and common knowledge of information partitions.
LSE Choice Group working paper series,
vol. 3, no. 6.
The Centre for Philosophy of Natural and Social Science (CPNSS), London, UK.
This paper addresses the question whether interactive knowledge and common knowledge of information partitions are additional assumptions in the state-space model of knowledge. Robert Aumann and others have already discussed this issue, but in a way that appears unsatisfactory. This paper provides a thorough answer to the question in four steps. First, it makes clear the methodological nature of the puzzles surrounding interactive and common knowledge of information partitions. Second, it points out two properties – labeled as Substitutivity and Immediacy – that knowledge holds in the state-space model, and that have received little attention in the literature. Third, based on the previous two steps, the paper demonstrates that interactive and common knowledge of information partitions are not additional assumptions of the state-space model of knowledge; this is the main contribution of the work. Finally, the Appendix of the paper offers a critical examination of Aumann’s discussion of the issue.
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