  We present a partial operator-theoretic characterization of approachability
principle and based on this characterization, we interpret a particular
distributed payoff allocation algorithm to be a sequence of time-varying
paracontractions. Further, we also propose a distributed algorithm, under the
context of coalitional game, on time-varying communication networks. The state
in the proposed algorithm converges to a consensus within, the predefined,
desired set. For convergence analysis, we rely on the operator-theoretic
property of paracontraction.
