Till now, we were considering the bargaining problems, where our aim was to define of how the players or economic agents should cooperate. What strategies should they choose in order to sign, for example, the cooperate or strategic agreement. In here, we will consider a problem of how to allocate cooperative payoff or joined payoff among the players so that their cooperation or cooperative agreement would be beneficial for all of the players. We will start with classical theoretical example called Jazz band. So, we have a club and the director of the club promises $100 for a performance to the singer, pianist and the drummer. But the question is how this group can allocate the payoff among themselves. Of course they could use the proportional approach. They could say that each of the participants should receive one third of the profit. But what if we know that the coalition of singer and pianist can earn $80. What if we know that the coalition of drummer and pianist can earn $65. What if we know that the pianist alone can earn $30, singer and drummer - $50, singer alone - $20 and the drummer alone cannot earn anything. Then what approach can we use? In order to answer that question, we need to define the so-called characteristic function of coalition S. So the characteristic function, shows the power or how much the coalition S can earn in the game. It is a real valued function which is defined on the set of subsets of the set N, which is set of coalitions of the players of the set N and it assigns a value to each coalition. The classical property or requirement for characteristic function is super additivity. The super additivity property means that if we take any two coalitions with no intersection between them and we calculate the characteristic function of these two coalitions together, then the value of this characteristic function will be more or equal than the sum of characteristic function of one coalition and the characteristic function of the second coalition. If this condition holds for any coalition distribution, then it would guarantee that all players would want to cooperate or would want to compose a grand coalition. So, all players would want to cooperate. We can define or we will define the cooperative game as a pair, N and v, where N is a set of players and v is a characteristic function, which is defined for each coalition. Let's consider the cooperative game for our example Jazz band. In here, the set of players is set of three players, singer, drummer and pianist and characteristic function is calculated according to the slide. So the characteristic function of a grand coalition or coalition one, two, three is equal to 100. It means that players of coalition one, two, three can earn $100. Characteristic function of coalition one and two is equal to 50, which means that singer and the drummer can earn $50. Coalition of players one and three which is singer and pianist is equal to 80. Characteristic function of drummer and pianist is equal to 65 and characteristic function of singer is equal to 20, characteristic function of a drummer is equal to zero because he cannot earn anything alone, and characteristic function of pianist is equal to 30. Now we can check if this so defined characteristic function is super additive. Let's do that for coalitions one, two and three and the characteristic function for coalition one, two is equal to 50, characteristic function for coalition three is equal to 30, that sum is equal to 80, and the characteristic function of a grand coalitions is equal to 100. So, 100 is more or equal than 80 which means that the super additivity condition is satisfied for this coalition distribution and in the same way, we can check for any coalition distributions. On this slide, you can see the list of references where you can get more information about the Jazz band model and also get more information about the super additivity property and characteristic function.