  Cooperative game theory deals with systems where players want to cooperate to
improve their payoffs. But players may choose coalitions in a non-cooperative
manner, leading to a coalition-formation game. We consider such a game with
several players (willing to cooperate) and an adamant player (unwilling to
cooperate) involved in resource-sharing. Here, the strategy of a player is the
set of players with whom it wants to form a coalition. Given a strategy
profile, an appropriate partition of coalitions is formed; players in each
coalition maximize their collective utilities leading to a non-cooperative
resource-sharing game among the coalitions, the utilities at the resulting
equilibrium are shared via Shapley-value; these shares define the utilities of
players for the given strategy profile in coalition-formation game. We also
consider the utilitarian solution to derive the price of anarchy (PoA). We
considered a case with symmetric players and an adamant player; wherein we
observed that players prefer to stay alone at Nash equilibrium when the number
of players (n) is more than 4. In contrast, in the majority of the cases, the
utilitarian partition is grand coalition. Interestingly the PoA is smaller with
an adamant player of intermediate strength. Further, PoA grows like O(n).
