A game-theoretic perspective on communication for omniscience

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.