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soln5 - and finish the game(2,0 player 1(1,0(0,0 u 1(win u...

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1 Solutions to Problem Set No. 5 1. Represent the game of Marienbad with a starting configuration of 3 matches in each pile in extensive form. Marienbad: There are two piles of matches and two players. The game starts with player 1 and thereafter the players take turns. When it is a player’s turn, he can remove any number of matches from either pile. Each player is required to remove some number of matches if either pile has matches remaining, and he can only remove matches from one pile at a time. The game of Marienbad is a game of perfect information because every information set has a single decision node in it. 2. Use backward induction to solve the game from a configuration of (1,0). What about (2,0) and (3,0)? The player starting at (1,0) loses because she can only remove the last match
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Unformatted text preview: and finish the game. (2,0) player 1 (1,0) (0,0) u 1 (win) u 1 (lose) u 2 (lose) u 2 (win) So, she will choose (1,0) and win. (3,0) player 1 (2,0) (1,0) (0,0) player 2 u 1 (win) u 1 (lose) u 2 (lose) u 2 (win) (1,0) (0,0) u 1 (lose) u 1 (win) u 2 (win) u 2 (lose) 2 3. (a) Solve the game by backward induction. There are two solutions using backward induction. node: (1.1), (1.2), (2.1), (2.2), (3.1), (3.2) <1> L M’ u m’ l c’ => (2,3,3) <2> M M’ u m’ l c’ => (2,3,1) (b) Find two alternative solutions. node: (1.1), (1.2), (2.1), (2.2), (3.1), (3.2) <1> L M’ d u’(or d’) l l’ (or r’) => (2,0,1) <2> R M’ u d’ l l’ => (1,3,5) If each believes that the other will carry out that strategy, then their own strategy is best....
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