Modeling Coordination Problems in a Music Ensemble: Some Logical and Game Theoretic Considerations

This paper considers in general terms, how musicians are able to coordinate through rational choices in a situation of (temporary) doubt in an ensemble performance. A fictitious example involving a 5-bar development in an unknown piece of music is analyzed in terms of epistemic logic, more specifically a multi-agent system, where it is shown that perfect coordination can only be certain to take place if the musicians have common knowledge of certain rules of the composition. We subsequently argue, however, that the musicians need not agree on the central features of the piece of music in order to coordinate. Such coordination can be described in terms of Michael Bacharach's theory of variable frames as an aid to solve game theoretic coordination problems.