Answer Happy

Suppose that each wind turbine needs an area of one acre and produces electricity that can be sold for one money unit. Our partial market has six agents. Four of them have one wind turbine each, and the two remaining agents have two acres of land each. The payoff of a coalition is the number of turbines that the members can run, i.e., the minimum of the number of turbine owners and two times the number of landowners in the coalition. For instance, if one or two wind turbine owners agree with one of the landowners to produce energy, then their payoff, i.e., their joint profit, is one or two money units, respectively. If all six agents form the grand coalition, then they can run the four wind turbines so that their payoff would be four, whereas the four wind turbine owners alone or the landowners alone have 0 payoffs. Model the foregoing decision problem as a cooperative transferable utility game (N, v) and compute and describe the core of (N, v).