Game theory

Mutual knowledge (logic)

Mutual knowledge is a fundamental concept about information in game theory, (epistemic) logic, and epistemology. An event is mutual knowledge if all agents know that the event occurred. However, mutual knowledge by itself implies nothing about what agents know about other agents' knowledge: i.e. it is possible that an event is mutual knowledge but that each agent is unaware that the other agents know it has occurred. Common knowledge is a related but stronger notion; any event that is common knowledge is also mutual knowledge. The philosopher Stephen Schiffer, in his book Meaning, developed a notion he called "mutual knowledge" which functions quite similarly to David K. Lewis's "common knowledge". Communications (verbal or non-verbal) can turn mutual knowledge into common knowledge. For example, in the Muddy Children Puzzle with two children (Alice and Bob, ), if they both have muddy face (viz. ), both of them know that there is at least one muddy face. Written formally, let , and then we have . However, neither of them know that the other child knows, which makes mutual knowledge. Now suppose if Alice tells Bob that she knows (so that becomes common knowledge, i.e. ), and then Bob tell Alice that he knows as well (so that becomes common knowledge, i.e. ), this will turn into common knowledge, which is equivalent to the effect of a public announcement "there is at least one muddy face". (Wikipedia).

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From playlist Logic & Philosophy of Mathematics

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From playlist SELF

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From playlist Information theory and Coding

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From playlist Philosophy

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From playlist Philosophy of Mind

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Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu

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Related pages

Dynamic epistemic logic | Common knowledge (logic) | Event (probability theory) | Induction puzzles | Game theory