Generalisation of Samet's (2010) agreement theorem

Tarbush, Bassel (2011): Generalisation of Samet's (2010) agreement theorem.

Abstract

We develop a framework that allows us to reproduce the generalised agreement theorem of Samet (2010), and extend it to models in which agents can base their decisions on false information, while highlighting the features that distinguish the result from the classic theorems found in the literature. For example, it allows decisions to be based on interactive information, and imposes no requirements on the language in which the states are described. Finally, we produce a result that does not require Samet’s assumption of the existence of a completely uninformed agent.

• 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

Aumann, R. J.: 1976, ‘Agreeing to disagree’. The annals of statistics 4(6), 1236–1239.

Aumann, R. J. and S. Hart: 2006, ‘Agreeing on decisions, The Hebrew University of Jerusalem’. Center for Rationality, unpublished DP.

Bacharach, M.: 1985, ‘Some extensions of a claim of Aumann in an axiomatic model of knowledge’. Journal of Economic Theory 37(1), 167–190.

Bonanno, G. and K. Nehring: 1998, ‘Assessing the Truth Axiom under incomplete information’. Mathematical social sciences 36(1), 3–29.

Cave, J. A.: 1983, ‘Learning to agree’. Economics Letters 12(2), 147–152.

Chellas, B. F.: 1980, Modal logic. Cambridge University Press Cambridge.

Hintikka, J.: 1962, Knowledge and belief: an introduction to the logic of the two notions. Cornell University Press.

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.

Samet, D.: 2010, ‘Agreeing to disagree: The non-probabilistic case’. Games and Economic Behavior 69(1), 169–174.

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

van Benthem, J.: 2010, ‘Modal Logic for Open Minds’. Center for the Study of Language and Information.