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# A2 - CSC 5350 Assignment 2 Due date 9 November 2008 1...

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CSC 5350 Assignment 2 Due date: 9 November 2008 1. Subgame perfect equilibrium can be defined using the one deviation property if the game has finite horizon. Show that this property does not hold for infinite horizon games. 2. Say that a finite extensive game with perfect information satisfies the no indifference condition if j z z for all j N whenever i z z for some i N , where z and z are terminal histories. Show, using induction on the length of subgames, that every player is indifferent among all subgame perfect equilibrium outcomes of such a game. Show also that if s and s are subgame perfect equilibria then so is  s , where for each player i the strategy  i s is equal to either i s or i s (i.e. the equilibria of the game are interchangeable ). 3. Two players agree to share a piece of cake using the following procedure. First, player 1 cuts the cake into two pieces. Then player 2 chooses one of these two pieces for himself (so that player 1 gets the one that player 2 does not choose). Each player prefers more of the cake to less.

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A2 - CSC 5350 Assignment 2 Due date 9 November 2008 1...

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