Editing Common knowledge (logic) (section)

== Applications ==
{{Unreferenced section|date=March 2022}}
Common knowledge was used by David Lewis in his pioneering game-theoretical account of convention. In this sense, common knowledge is a concept still central for linguists and philosophers of language (see Clark 1996) maintaining a Lewisian, conventionalist account of language.

[[Robert Aumann]] introduced a set theoretical formulation of common knowledge (theoretically equivalent to the one given above) and proved the so-called [[Aumann's agreement theorem|agreement theorem]] through which: if two agents have common [[prior probability]] over a certain event, and the [[posterior probabilities]] are common knowledge, then such posterior probabilities are equal. A result based on the agreement theorem and proven by Milgrom shows that, given certain conditions on market efficiency and information, speculative trade is impossible.

The concept of common knowledge is central in [[game theory]]. For several years it has been thought that the assumption of common knowledge of rationality for the players in the game was fundamental. It turns out (Aumann and Brandenburger 1995) that, in two-player games, common knowledge of rationality is not needed as an epistemic condition for [[Nash equilibrium]] [[strategy (game theory)|strategies]].

Computer scientists use languages incorporating epistemic logics (and common knowledge) to reason about distributed systems. Such systems can be based on logics more complicated than simple propositional epistemic logic, see Wooldridge ''Reasoning about Artificial Agents'', 2000 (in which he uses a first-order logic incorporating epistemic and temporal operators) or van der Hoek et al. "Alternating Time Epistemic Logic".

In his 2007 book,  ''[[The Stuff of Thought|The Stuff of Thought: Language as a Window into Human Nature]],'' [[Steven Pinker]] uses the notion of common knowledge to analyze the kind of indirect speech involved in innuendoes.<ref>{{cite arXiv |eprint=2310.00264 |last1=Liang |first1=Xiaolong |last2=Wáng |first2=Yì N. |title=Epistemic Logic over Similarity Graphs: Common, Distributed and Mutual Knowledge |date=2023 |class=cs.LO }}</ref>