5. THREE PLAYER MAJORITY GAME (15PTs) Consider a variant of the three player majority game we introduced in class. The three players, 1, 2, and 3, again need to decide how to allocate one unit of resources amongst themselves by voting. However, now player 1 has 1 vote, player 2 has 2 votes, and player 3 has three votes. To pass a proposed allocation, at least four votes is required. So, any coalition that does not possess at least four votes has only one action that gives each of its members zero resources, while any coalition that does possess at least four votes can choose any allocation of the one unit of resources amongst its members (e.g., an action of the grand coalition is simply an allocation (331, 302, 3:3) such that 3:,- 2 0 for all i and $1 + :62 + 3123 S 1). Find the core of this game. Characterize it and defend your