The assignment problem as a cooperative game

We consider the problem of optimal distribution of assignments between workers on machines. Workers can exchange machines with the aim of saving the total time to execute the assignments, compared to their initial distribution. It is proved that the corresponding cooperative game has a non-empty c-core and is totally balanced. Based on the Hungarian method of solving the assignment problem, an algorithm for constructing an imputation from the c-core is formulated. In the case of an integer characteristic function, the algorithm constructs an imputation from the c-core with integer components. This result is generalized to the case of arbitrary totally balanced games of three and four persons, as well as for symmetric games.