Collaboration and Mutual Knowledge

If two people, Alice and Bob, are working towards the same goal without awareness of each other's activities, are they collaborating? We might loosely refer to them as such, but "working together" typically means more than working towards the same goal. Yet it does not require that the work be performed in partnership at the same time and in the same place. Alice and Bob can "work together" even though they may be separated physically and temporally. Alice and Bob can "work together" without having been introduced and without knowledge of each other's identity. Alice and Bob can "work together" even though they each speak a different language. So what is the essence of collaboration?

Collaboration most clearly occurs when the act of working together is mutually known.

Mutual Knowledge Defined

Alice and Bob have mutual knowledge¹ of a thing, which I will call X, when:

• Alice knows X, and Bob knows X
• Alice knows that Bob knows X, and Bob knows that Alice knows X
• Alice knows that Bob knows that Alice knows X, and Bob knows that Alice knows that Bob knows X
• and so on, ad infinitum

Thus we can say with confidence that Bob and Alice are working collaboratively if:

•  X=Alice and Bob are working towards a specified goal, and
• Bob and Alice mutually know X

In general, mutual knowledge allows collaborators to co-ordinate their work.  However, there are cases of collaboration based on something less than mutual knowledge.  For example, if Bob is working towards a goal and knows that Alice also is working towards that goal, then Bob might be said to be working in collaboration with Alice, even though Alice herself is not working in collaboration with anyone.  Similarly, if Alice and Bob each are aware that some other party is working towards a specified goal, they may be said to be working collaboratively, even if they are not aware of each other's existence.  Exploring cases like these may help us to understand the collaborative process.

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¹Herbert Clark and I used the term "mutual knowledge" in: Clark, H. H. & Marshall, C. R. (1978). Reference diaries (pp. 57-63). In D. L. Waltz (Ed.), Theoretical issues in natural language processing (Vol. 2). New York: Association for Computing Machinery. PDF

The term "mutual knowlege" has been used in the same way by other researchers in the fields of cognitive science and linguistics. The terms "common ground" and "common knowledge" are sometimes used to describe the same concept, but these terms have other meanings in other contexts (as does the term "mutual knowledge" in the context of game theory).  Since there is no universal agreement on a term to describe the concept presented above, I will stick with "mutual knowledge."