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.
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| - Mutual knowledge (logic) (en)
- Взаимное знание (ru)
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| - 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. (en)
- Взаимное знание (англ. mutual knowledge) — концепция эпистемической теории игр, эпистемической модальной логики и эпистемологии. Событие является взаимным знанием, если о его наступлении известно всем участникам игры. От общего знания взаимное отличается тем, что вне рассмотрения остаётся осведомлённость игроков о знаниях соперников, о знаниях об осведомлённости и так далее ad infinitum. Таким образом, общее знание является более сильным условием, и всякое общее знание является взаимным. (ru)
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| - 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". (en)
- Взаимное знание (англ. mutual knowledge) — концепция эпистемической теории игр, эпистемической модальной логики и эпистемологии. Событие является взаимным знанием, если о его наступлении известно всем участникам игры. От общего знания взаимное отличается тем, что вне рассмотрения остаётся осведомлённость игроков о знаниях соперников, о знаниях об осведомлённости и так далее ad infinitum. Таким образом, общее знание является более сильным условием, и всякое общее знание является взаимным. Термин «взаимное знание» использовался философом Стивеном Шиффером для именования собственной концепции (1972), однако содержательно она была идентична «общему знанию» Дэвида Келлогга Льюиса (1969). (ru)
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