Common knowledge and limit knowledge

Bach, Christian W.; Cabessa, Jérémie

doi:10.1007/s11238-011-9257-4

Cited by 3 publications

(7 citation statements)

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“…Such a descriptive use of topologies is in line with Rubinstein's [22] view that topology can be used as a substantial tool to formalize natural intuitions about closeness. 4 In this context, Bach and Cabessa [7,8] consider Aumann structures equipped with topologies 5 on the event space and introduce the operator limit knowledge, which is linked to epistemic features as well as topological aspects of the event space. More precisely, limit knowledge is defined as the topological limit of higher-order mutual knowledge.…”

Section: An Epistemic-topological Approach To Agreeing To Disagreementioning

confidence: 99%

“…The operator limit knowledge is shown by Bach and Cabessa [7,8] to be able to provide relevant epistemic-topological characterizations of solution concepts in games. Despite being based on the same sequence of higher-order mutual knowledge claims, the distinguished interest of limit knowledge resides in its capacity to potentially differ from the purely epistemic operator common knowledge.…”

Section: An Epistemic-topological Approach To Agreeing To Disagreementioning

confidence: 99%

“…CK(E) ⊆ E, the epistemic-topological operator limit knowledge does in general not bear this property. 8 However, if the sequence of higher-order mutual knowledge of some event E is not strictly shrinking, then limit knowledge is equal to common knowledge, and therefore, limit knowledge is factive, i.e. LK(E) ⊆ E. 9 In particular, limit knowledge is factive in all finite Aumann structures.…”

Section: An Epistemic-topological Approach To Agreeing To Disagreementioning

confidence: 99%

“…Here, we analyse agreeing to disagree in a topologically extended epistemic framework. The epistemic operator common knowledge is replaced by the epistemic-topological operator limit knowledge introduced by Bach and Cabessa [7,8]. Assuming common priors, Bayesian agents and limit knowledge of posteriors, we derive a possibility result allowing the agents' posteriors to differ.…”

Section: Introductionmentioning

confidence: 99%

“…Aumann's agreement theorem is then given in two slightly modified formulations and graphically illustrated. Section 3 sketches the topological approach to interactive epistemology initiated by Bach and Cabessa [7,8]. Moreover, the epistemic-topological operator limit knowledge is defined and used for a possibility result on agreeing to disagree.…”

Section: Introductionmentioning

confidence: 99%

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Limit-agreeing to disagree <xref ref-type="fn" rid="FN14">*</xref>

Bach

Cabessa

2016

Journal of Logic and Computation

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We reconsider Aumann' s seminal impossibility theorem that agents cannot agree to disagree in a topologically extended epistemic model. In such a framework, a possibility result on agreeing to disagree actually ensues. More precisely, agents with a common prior belief satisfying limit knowledge instead of common knowledge of their posterior beliefs may have distinct posterior beliefs. Since limit knowledge is defined as the limit of iterated mutual knowledge, agents can thus be said to limit-agree to disagree. Besides, an example is provided in which limit knowledge coincides with Rubinstein's (1989) notion of almost common knowledge, and the agents have almost common knowledge of posteriors yet distinct posterior beliefs. More generally, an epistemic-topological foundation for almost common knowledge is thus provided.

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