Sequencing games with repeated players (Q926369)

Consider a sequencing situation in which a finite set of players, \(N\), are assigned to a finite set of jobs, \(M\), in a certain sequence, \(s\), with an attached cost profile \(c(s)\). Let \((N, v)\) be the cooperative game associated with the sequencing situation, where \(v(S)\) maximizes cost savings for coalition \(S\) to fill all jobs. The paper considers two types of cooperative game: (1) max, in which case each player's cost is linear in maximum completion time of his jobs; (2) min, in which case each player's cost is linear in minimum completion time of his jobs. The paper constructs rule sequences such that both max and min have non-empty cores, and the job sequence so constructed is in the core. In addition, min is a convex game, and so has a large core.