  We offer a new approach to the information decomposition problem in
information theory: given a 'target' random variable co-distributed with
multiple 'source' variables, how can we decompose the mutual information into a
sum of non-negative terms that quantify the contributions of each random
variable, not only individually but also in combination? We derive our
composition from cooperative game theory. It can be seen as assigning a "fair
share" of the mutual information to each combination of the source variables.
Our decomposition is based on a different lattice from the usual 'partial
information decomposition' (PID) approach, and as a consequence our
decomposition has a smaller number of terms: it has analogs of the synergy and
unique information terms, but lacks terms corresponding to redundancy. Because
of this, it is able to obey equivalents of the axioms known as 'local
positivity' and 'identity', which cannot be simultaneously satisfied by a PID
measure.
