chapter6 - Adversarial Search and GamePlaying CHAPTER 6...

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CHAPTER 6 CMPT 310: SPRING 2011 HASSAN KHOSRAVI Adversarial Search and Game- Playing
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Adversarial Search Examine the problems that arise when we try to plan ahead in a world where other agents are planning against us. A good example is in games.
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Search versus Games Search no adversary Solution is (heuristic) method for finding goal Heuristics and CSP techniques can find optimal solution Evaluation function: estimate of cost from start to goal through given node Examples: path planning, scheduling activities Games adversary Solution is strategy (strategy specifies move for every possible opponent reply). Time limits force an approximate solution Evaluation function: evaluate “goodness” of game position Examples: chess, checkers, Othello, backgammon
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Types of Games
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Prisoner’s Dilemma Confess Don’t Confess prisoner1 Prisoner2 Confess Don’t Confess ( -8, -8) ( -15, 0) ( 0, -15) ( -1, -1)
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Prisoner’s Dilemma Confess Don’t Confess prisoner1 Prisoner2 Confess Don’t Confess ( -8 , -8) ( -15 , 0) ( 0, -15) ( -1, -1)
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Prisoner’s Dilemma Confess Don’t Confess prisoner1 Prisoner2 Confess Don’t Confess ( -8, -8) ( -15, 0) ( 0 , -15) ( -1 , -1)
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Prisoner’s Dilemma Conclusion: The prisoner1 will confess And Prisoner2 ?
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Prisoner’s Dilemma Confess Don’t Confess prisoner1 Prisoner2 Confess Don’t Confess ( -8, -8 ) ( -15, 0) ( 0, -15 ) ( -1, -1)
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Prisoner’s Dilemma Confess Don’t Confess prisoner1 Prisoner2 Confess Don’t Confess ( -8, -8 ) ( -15, 0) ( 0, -15) ( -1, -1)
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Prisoner’s Dilemma Conclusion: Prisoner2 confesses also Both get 8 years, even though if they cooperated, they could get off with one year each For both, confession is a dominant strategy: a strategy that yields a better outcome regardless of the opponent’s choice
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Game Setup Two players: MAX and MIN MAX moves first and they take turns until the game is over Winner gets award, loser gets penalty. Games as search: Initial state: e.g. board configuration of chess Successor function: list of (move,state) pairs specifying legal moves. Terminal test: Is the game finished? Utility function: Gives numerical value of terminal states. E.g. win (+1), lose (-1) and draw (0) in tic-tac-toe or chess MAX uses search tree to determine next move.
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Size of search trees b = branching factor d = number of moves by both players Search tree is O(b d ) Chess b ~ 35 D ~100 - search tree is ~ 10 154 (!!) - completely impractical to search this Game-playing emphasizes being able to make optimal decisions in a finite amount of time Somewhat realistic as a model of a real-world agent Even if games themselves are artificial
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chapter6 - Adversarial Search and GamePlaying CHAPTER 6...

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