Agreeing to disagree.

  title={Agreeing to disagree.},
  author={R. Aumann},
  journal={Nature cell biology},
  volume={8 8},
  • R. Aumann
  • Published 2006
  • Mathematics, Medicine
  • Nature cell biology
Two people, 1 and 2, are said to have common knowledge of an event E if both know it, 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on. 
On Logic of Belief-Disagreement among Agents
Epistemic disagreement and agreement between two agents have been considered by game theorists and logicians[1][2]. But they are discussed only from the view of knowledge.
Aggregate information , common knowledge and agreeing not to bet ∗
This note considers gambles that take place even if only some – but not all – individuals agree to participate. I show that the bet cannot take place if it is commonly known how many individuals areExpand
Strong belief and agreeing to disagree
In this paper, we extend Aumann’s agreement theorem to a framework where beliefs are modeled by a conditional probability system a la Battigalli and Siniscalchi (1999). Indeed, if posterior beliefsExpand
Direct and Indirect Common Belief
We give informal definitions of the concepts of direct and indirect common belief, illustrating them by an example. We then provide an analysis of these concepts within public announcement logicExpand
Possibility to agree on disagree from quantum information and decision making
The celebrated Aumann theorem states that if two agents have common priors, and their posteriors for a given event E are common knowledge, then their posteriors must be equal; agents with the same ...
Agreeing to disagree without the countable additivity axiom
An example is given in which agents “agree to disagree”. It relies on the absence of the countable additivity axiom.
Agreeing to disagree: The non-probabilistic case
  • D. Samet
  • Mathematics, Computer Science
  • Games Econ. Behav.
  • 2010
A non-probabilistic generalization of Aumann's agreement theorem is proved based on a new version of the sure-thing principle that makes an interpersonal-intrastate comparison of knowledge. Expand
Agreeing to agree and Dutch books
It is shown that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. Expand
Logic for Describing Strong Belief-Disagreement Between Agents
The notion of belief-disagreement as well as belief-agreement can facilitate gaining a clearer understanding of the acts of trade and speech. Expand
Intersubjective Consistency Of Beliefs And The Logic Of Common Belief
We characterize the class of n-person belief systems for which common belief has the properties of the strongest logic of belief, KD45. The characterizing condition states that individuals are notExpand


We Can't Disagree Forever
Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will convergeExpand
Probability and the Art of Judgment
Preface 1. Introduction: radical probabilism 2. Valuation an dacceptance of scientific hypotheses 3. Probable knowledge 4. Probability and the art of judgment 5. Bayesianism with a human face 6.Expand
Reaching a Consensus
Abstract Consider a group of individuals who must act together as a team or committee, and suppose that each individual in the group has his own subjective probability distribution for the unknownExpand
Judgment under Uncertainty: Heuristics and Biases.
Three heuristics that are employed in making judgements under uncertainty are described: representativeness, availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development. Expand
Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game
Parts I and II of this paper have described a new theory for the analysis of games with incomplete information. Two cases have been distinguished: consistent games in which there exists some basicExpand
Subjectivity and Correlation in Randomized Strategies
Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of aExpand
COMPETITIVE EQUILIBRIUM UNDER UNCERTAINTY11This research was supported in part by the Office of Naval Research under Contract ONR 222(77) with the University of California. Reproduction in whole or in part is permitted for any purpose of the United States Government.
This paper extends the general equilibrium analysis of the previous reading by examining the states of nature that particular individuals are capable of distinguishing. Equilibrium is examined underExpand
Agreeing to disagree.
Interactive Epistemology
  • Discussion Paper No. 67,
  • 1995
Information and Competitive Price Systems