The 1/4-core of the uniform bin packing game is nonempty

A cooperative bin packing game is an N -person game, where the player set N consists of k bins of capacity 1 each and n items of sizes $a_1,\dots,a_n$. The value of a coalition of players is defined to be the maximum total size of items in the coalition that can be packed into the bins of the coalition. We adopt the taxation model proposed by Faigle and Kern (1993) [6] and show that the 1/4-core is nonempty for all instances of the bin packing game. This strengthens the main result in [3]