Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes ; players 2 and 3 vote Y or N. Two Y votes implement it; two N reject it; with one Y and one N, player 1 casts the deciding vote. If 1's proposal is rejected, 2 makes a proposal on which only 3 votes: if 3 votes Y it passes, if 3 votes N it is rejected and is implemented. If a player's expected allocation is the same whether she votes Y or N, she votes N.
1's proposal will be:
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Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes (x₁,x₂,x₃); players 2 and 3 vote Y or N. Two Y votes implement it; two N reject it; with one Y and one N, player 1 casts the deciding vote. If 1's proposal is rejected, 2 makes a proposal on which only 3 votes: if 3 votes Y it passes, if 3 votes N it is rejected and (3,3,3) is implemented. If a player's expected allocation is the same whether she votes Y or N, she votes N. 1's proposal will be: (A) (5,0,4) (B) (4,0,5) (C) (3,6,0) (D) (6,3,0)
Also written as: Three players 1, 2, 3 allocate 9 indivisible coins. Player 1 proposes (x_1,x_2,x_3); players 2 and 3 vote Y or N. Two Y votes implement it; two N reject it; with one Y and one N, player 1 casts the deciding vote. If 1's proposal is rejected, 2 makes a proposal on which only 3 votes: if 3 votes Y it passes, if 3 votes N it is rejected and (3,3,3) is implemented. If a player's expected allocation is the same whether she votes Y or N, she votes N. 1's proposal will be:
Game theory and strategic behaviour has come up 61 times in 6 exams since 2008.
This question is on Extensive-form games and backward induction, part of Game theory and strategic behaviour in Game Theory.
Games played in sequence, solved from the end back to the start.
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