Variant of the 3-Player Majority Game - Consider a coalitional game where 5, instead of 3, players need to decide on how to allocate one unit of resources. They will decide on the allocation via a vote, where each player has one vote and a simple majority (3 votes) is required to pass a resolution. Thus, any coalition with two players or less has only one action that gives themselves no resources, while any

coalition with three players or more can allocate the resources anyway they like.

(a) What is the core of this game? Justify your answer.

(b) Now suppose Players 1,2 and 3 have formed a pact and will always vote the same

way. We can treat this situation as a three player game where one of them has three votes and the other two each have one vote. What is the core of this new game? Justify your answer.