In the sink problem (Example 6.8), we took the characteristic function v(i) = 0, v(12) = 105,…

In the sink problem (Example 6.8), we took the characteristic function v(i) = 0, v(12) = 105, v(13) = 120, v(23) = 135, and v(123) = 150, which models the fact that the players get the number of sinks each coalition can load and anyone not in the coalition would get nothing. The truck capacity and least core allocation in this case was

(a) Suppose that each coalition now gets the sinks left over after anyone not in the coalition gets their full truck capacity met first. Curly will help load any one player coalition. What is the characteristic function?

(b) Show that the core of this game is not empty and find the least core.