Agreement theorems with interactive information: possibilities and impossibilities

Tarbush, Bassel (2011): Agreement theorems with interactive information: possibilities and impossibilities.

Abstract

Following from Tarbush (2011a), we explore the implications of using two different definitions of informativeness over kens; one that ranks objective, and the other subjective information. With the first, we create a new semantic operation that allows us to derive agreement theorems even when decision functions are based on interactive information (for any r ≥ 0). Effectively, this operation, unlike information cell union captures the notion of an agent becoming “more ignorant” for all modal depths. Using the definition that ranks subjective information however, we show an impossibility result: In generic models, agreement theorems using the standard Sure-Thing Principle do not hold when decision functions depend on interactive information (when r > 0).

• Item Type: MPRA Paper
• Language: English
• Keywords: Agreeing to disagree; knowledge; common knowledge; belief; information; epistemic logic
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D89 - Other; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General

References

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Moses, Y. and G. Nachum: 1990, ‘Agreeing to disagree after all’. In: Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge. pp. 151–168.

Tarbush, B.: 2011a, ‘Agreeing to disagree: a syntactic approach’. University of Oxford, Department of Economics, Working Paper.

Tarbush, B.: 2011b, ‘Generalisation of Samet’s (2010) agreement theorem’. University of Oxford, Department of Economics, Working Paper.