Identify the sub game perfect equilibrium of this game

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Three players 1,2, and 3, are deciding on how to divide a cake worth $1, using the following procedure: Player 1 first divides the cake into three portions: x,y,and z such that x+y+z=1, x,y,z greater than or equal to 0. Player 2 then picks which of the three portions to consume. Next, player 3 picks the picks the one from the remaining two portions, followed by player 1 consuming the last one left.

a) Identify the sub game perfect equilibrium of this game. How will player 1 divide the cake?

b) Suppose that player 1 picks his portion before player 3 does (with the rest of the procedure unchanged). Identify the sublime perfect equilibrium of this game. How will player 1 divide the cake?

Reference no: EM13898655

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