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asgn2_sol

# asgn2_sol - CSC 5350 Assignment 2 1 2 3(a N= cfw_1 2 A1...

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CSC 5350 Assignment 2 1.

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2.
3. (a) N = {1, 2} A 1 = [1/2, 1] (The action ߣא ܣ means that player 1 cuts the cake into 2 pieces, and ߣ is the proportion of the larger piece. Suppose the cake is 1 unit.) A 2 = {L, S} (L: player 2 chooses the larger piece. S: player 2 chooses the smaller piece.) ܲሺ׎ሻൌ1 ,ܲሺ݄ሻൌ2 if length of h is 1. ܪൌ ሼ׎ሽ׫ቂ ,1ቃ׫ሼሺߣ, ܽሻ: ߣ א ቂ ,1ቃ,ܽאሼܮ, ܵሽሽ ሺߣ ,ܵሻ ؼ ሺߣ ,ܮሻ, ሺߣ ,ܮሻ ؼ ሺߣ ,ܵሻ If A 1 = ½, then player 2 will be indifferent in either piece. The extensive game is as follows: (b) The subgame perfect equilibrium can be determined using backward induction. In the subgame ߁ሺߣሻ, where ߣ א ܣ , player 2 will always choose L because he prefers the larger piece. Then player 1’s payoff will be maximized when ߣ ൌ 1/2 .

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asgn2_sol - CSC 5350 Assignment 2 1 2 3(a N= cfw_1 2 A1...

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