Question 6 [20 marks] A game (N, v) is simple if for every coalition SC N, either v(S) = 0 or v(S) = 1. In a simple game

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Question 6 20 Marks A Game N V Is Simple If For Every Coalition Sc N Either V S 0 Or V S 1 In A Simple Game 1 (47.44 KiB) Viewed 40 times

Question 6 [20 marks] A game (N, v) is simple if for every coalition SC N, either v(S) = 0 or v(S) = 1. In a simple game, a player, t, is said to be a veto player, if v(N\ {i}) = 0. (a) Suppose (N. v) is a simple game with u(N) = 1, and suppose there are no veto players in (N. v). Prove that the core of this game is empty. (b) Consider a corporation with n stock-holders in which stock-holder 1 has 2n - 3 shares and stock-holders 2 to n have 2 shares each. Any decision can be settled by approval of stock-holders holding a simple majority of the shares, i.c. by a coalition holding > 50% shares. (i) Find the core of this game. (ii) Find the Shapley value of this game.