  We propose a coalition game model for the problem of communication for
omniscience (CO). In this game model, the core contains all achievable rate
vectors for CO with sum-rate being equal to a given value. Any rate vector in
the core distributes the sum-rate among users in a way that makes all users
willing to cooperate in CO. We give the necessary and sufficient condition for
the core to be nonempty. Based on this condition, we derive the expression of
the minimum sum-rate for CO and show that this expression is consistent with
the results in multivariate mutual information (MMI) and coded cooperative data
exchange (CCDE). We prove that the coalition game model is convex if the
sum-rate is no less than the minimal value. In this case, the core is non-empty
and a rate vector in the core that allocates the sum-rate among the users in a
fair manner can be found by calculating the Shapley value.
