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 3 votes. To pass a proposed allocation, at least five votes are required. So, any coalition that does not possess at least five votes has only one action that gives each of its members zero resources, while any coalition that does possess at least five 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 (x1, x2, x3) such that xi ≥ 0 for all i is the portion of resources allocated to player i and x1 + x2 + x3 ≤ 1). Find the core of this gam
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 3 votes. To pass a proposed allocation, at least five votes are required. So, any coalition that does not possess at least five votes has only one action that gives each of its members zero resources, while any coalition that does possess at least five 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 (x1, x2, x3) such that xi ≥ 0 for all i is the portion of resources allocated to player i and x1 + x2 + x3 ≤ 1). Find the core of this game.
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