Tarbush, Bassel (2011): Agreeing to disagree with generalised decision functions.
Download (673Kb) | Preview
We develop a framework that allows us to emulate standard results from the “agreeing to disagree" literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). We analyse the implications of the Sure-Thing Principle, a central assumption. The upshot is that the way in which states are described matters, and that the results fail if decisions are allowed to depend on interactive information. Furthermore, using very weak additional assumptions, we extend all previous results to models with a non-partitional information structure in a coherent manner. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle.
|Item Type:||MPRA Paper|
|Original Title:||Agreeing to disagree with generalised decision functions|
|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
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General
|Depositing User:||bassel tarbush|
|Date Deposited:||27. Feb 2011 07:00|
|Last Modified:||01. Mar 2013 10:42|
Aumann, R. J.: 1976, ‘Agreeing to disagree’. The annals of statistics 4(6), 1236–1239.
Aumann, R. J.: 1987, ‘Correlated equilibrium as an expression of Bayesian rationality’. Econometrica: Journal of the Econometric Society 55(1), 1–18.
Aumann, R. J.: 1999, ‘Interactive epistemology I: knowledge’. International Journal of Game Theory 28(3), 263–300.
Aumann, R. J. and S. Hart: 2006, ‘Agreeing on decisions, The Hebrew University of Jerusalem’. Center for Rationality, unpublished DP.
Aumann, R. J., S. Hart, and M. Perry: 2005, ‘Conditioning and the Sure-Thing Principle, The Hebrew University of Jerusalem’. Center for Rationality, DP-393.
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.
Collins, J.: 1997, ‘How we can agree to disagree’. Online Working Paper.
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.: 1990, ‘Ignoring ignorance and agreeing to disagree’. Journal of Economic Theory 52(1), 190–207.
Samet, D.: 2010, ‘Agreeing to disagree: The non-probabilistic case’. Games and Economic Behavior 69(1), 169–174.
Shafir, E.: 1994, ‘Uncertainty and the difficulty of thinking through disjunctions’. Cognition 50(1-3), 403–430.
Tarbush, B.: 2011, ‘Generalisation of Samet’s (2010) agreement theorem’. 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.
Available Versions of this Item
- Agreeing to disagree with generalised decision functions. (deposited 27. Feb 2011 07:00) [Currently Displayed]