A river has n pollution-producing factories dumping water into the river. Assume that the factory…

A river has n pollution-producing factories dumping water into the river. Assume that the factory does not have to pay for the water it uses, but it may need to expend money to clean the water before it can use it. Assume the cost of a factory to clean polluted water before it can be used is proportional to the number of polluting factories. Let c = cost per factory. Assume also that a factory may choose to clean the water it dumps into the river at a cost of b per factory. We take the inequalities 0

Take n = 5, b = 3,c = 2. Find the Shapley allocation