(Figure 1)

Villages A, B, C and D are located in a remote area and need to be connected to the main power line to be able to receive electricity for their respective populations

Use the principles of co-operative game theory to determine a fair allocation of cost for each village in order for all the villages to receive electricity. Please show all working when answering the following questions:

a) Find all the characteristic functions

b) Is the core empty, have a unique point or have a set of infinite points? Justify your answer.

c) Calculate the Shapley values in order to allocate costs to the four villages.

d) Is there a simplier way to determine the allocation of costs? Justify your answer.

e) Is the coalition of the 4 villages stable? Justify your answer.

f) From your calculations, summarize your recommendations to the four villages.

Power Line Power Line