The core and bargaining set of classical cooperative game are expanded, and the generalized core and bargaining set are defined. The models of the generalized proportional distribution and the reduced game are provided, the correspondence between average monotonic game and generalized reduced game is discussed, and the inclusion relationship between generalized proportional distribution and generalized core is provided. The equivalence property of the generalized core and bargaining set in average monotonic game is proved. The result not only enriches the study of solutions in cooperative game and application requirements in the field of profit reallocation, but also provides the nonempty property of the generalized core in the average monotonic game, which indicates that the optimal reallocation scheme is existent.