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.: 73  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, G = { a , b } {\displaystyle G=\{a,b\}} ), if they both have muddy face (viz. M a ∧ M b {\displaystyle M_{a}\land M_{b}} ), both of them know that there is at least one muddy face. Written formally, let p = [ ∃ x ∈ G ( M x ) ] {\displaystyle p=[\exists x\!\in \!G(M_{x})]} , and then we have K a p ∧ K b p {\displaystyle K_{a}p\land K_{b}p} . However, neither of them know that the other child knows ( ( ¬ K a K b p ) ∧ ( ¬ K b K a p ) {\displaystyle (\neg K_{a}K_{b}p)\land (\neg K_{b}K_{a}p)} ), which makes p = [ ∃ x ∈ G ( M x ) ] {\displaystyle p=[\exists x\!\in \!G(M_{x})]} mutual knowledge. Now suppose if Alice tells Bob that she knows p {\displaystyle p} (so that K a p {\displaystyle K_{a}p} becomes common knowledge, i.e. C G K a p {\displaystyle C_{G}K_{a}p} ), and then Bob tells Alice that he knows p {\displaystyle p} as well (so that K b p {\displaystyle K_{b}p} becomes common knowledge, i.e. C G K b p {\displaystyle C_{G}K_{b}p} ), this will turn p {\displaystyle p} into common knowledge ( C G E G p ⇒ C G p {\displaystyle C_{G}E_{G}p\Rightarrow C_{G}p} ), which is equivalent to the effect of a public announcement "there is at least one muddy face".