In selfish bin packing, each item is regarded as a player, who aims to
minimize the cost-share by choosing a bin it can fit in. To have a least number
of bins used, cost-sharing rules play an important role. The currently best
known cost sharing rule has a lower bound on PoA larger than 1.45, while a
general lower bound 4/3 on PoA applies to any cost-sharing rule under which
no items have incentive unilaterally moving to an empty bin. In this paper, we
propose a novel and simple rule with a PoA matching the lower bound, thus
completely resolving this game. The new rule always admits a Nash equilibrium
and its PoS is one. Furthermore, the well-known bin packing algorithm BFD
(Best-Fit Decreasing) is shown to achieve a strong equilibrium, implying that a
stable packing with an asymptotic approximation ratio of 11/9 can be produced
in polynomial time