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Extensive Form Games and Backward Induction

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Extensive Form Games and Backward Induction Recap Perfect-Information Extensive-Form Games Extensive Form Games and Backward Induction ISCI 330 Lecture 11 February 13, 2007 Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 1 Recap Perfect-Information Extensive-Form Games Lecture Overview Recap Perfect-Information Extensive-Form Games Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 2 I The extensive form is an alternative representation that makes the temporal structure explicit. I Two variants: I perfect information extensive-form games I imperfect-information extensive-form games Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 3 I Two variants: I perfect information extensive-form games I imperfect-information extensive-form games Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players I The extensive form is an alternative representation that makes the temporal structure explicit. Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 3 Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players I The extensive form is an alternative representation that makes the temporal structure explicit. I Two variants: I perfect information extensive-form games I imperfect-information extensive-form games Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 3 I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 I Terminal nodes are labeled with utility outcomes Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 Recap Perfect-Information Extensive-Form Games Perfect-Information Extensive Form Representation I Represents a finite sequential game as a rooted tree I Each internal node represents a particular player’s ’turn’ I Each branch from this internal node represents a different choice for that player I Each terminal node represents a possible final outcome of the game I Usually written with the basal root on top I Parts of the tree are labeled as follows: I Internal nodes (including the root) are labeled with player identifiers I Branches are labeled with player choices I Terminal nodes are labeled with utility outcomes Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 4 Get with a partner and decide on a simple sequential game (e.g. tic-tac-toe) and represent it in extended form Recap Perfect-Information Extensive-Form Games Example: the sharing game 1 ¨¨HH ¨ q H ¨¨ HH ¨ H 0–21–12–0 ¨¨ HH ¨¨ HH 222 ¡A ¡A ¡A ¡ A ¡ A ¡ qqq A ¡ A ¡ A ¡ A yesnoyesnoyesno ¡ A ¡ A ¡ A ¡ A ¡ A ¡ A (0,2)(0,0)(1,1)(0,0)(2,0)(0,0) qqqqqq Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 5 Recap Perfect-Information Extensive-Form Games Example: the sharing game 1 ¨¨HH ¨ q H ¨¨ HH ¨ H 0–21–12–0 ¨¨ HH ¨¨ HH 222 ¡A ¡A ¡A ¡ A ¡ A ¡ qqq A ¡ A ¡ A ¡ A yesnoyesnoyesno ¡ A ¡ A ¡ A ¡ A ¡ A ¡ A (0,2)(0,0)(1,1)(0,0)(2,0)(0,0) qqqqqq Get with a partner and decide on a simple sequential game (e.g. tic-tac-toe) and represent it in extended form Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 5 Recap Perfect-Information Extensive-Form Games Lecture Overview Recap Perfect-Information Extensive-Form Games Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 6 Play as a fun game, dividing 100 dollar coins. (Play each partner only once.) Recap Perfect-Information Extensive-Form Games Example: the sharing game 1 ¨¨HH ¨ q H ¨¨ HH ¨ H 0–21–12–0 ¨¨ HH ¨¨ HH 222 ¡A ¡A ¡A ¡ A ¡ A ¡ qqq A ¡ A ¡ A ¡ A yesnoyesnoyesno ¡ A ¡ A ¡ A ¡ A ¡ A ¡ A (0,2)(0,0)(1,1)(0,0)(2,0)(0,0) qqqqqq Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 7 Recap Perfect-Information Extensive-Form Games Example: the sharing game 1 ¨¨HH ¨ q H ¨¨ HH ¨ H 0–21–12–0 ¨¨ HH ¨¨ HH 222 ¡A ¡A ¡A ¡ A ¡ A ¡ qqq A ¡ A ¡ A ¡ A yesnoyesnoyesno ¡ A ¡ A ¡ A ¡ A ¡ A ¡ A (0,2)(0,0)(1,1)(0,0)(2,0)(0,0) qqqqqq Play as a fun game, dividing 100 dollar coins. (Play each partner only once.) Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 7 I player 1: 3; player 2: 8 I Overall, a pure strategy for a player in a perfect-information game is a complete specification of which deterministic action to take at every node belonging to that player. I Can think of a strategy as a complete set of instructions for a proxy who will play for the player in their abscence Recap Perfect-Information Extensive-Form Games Pure Strategies I In the sharing game (splitting 2 coins) how many pure strategies does each player have? Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 8 I Overall, a pure strategy for a player in a perfect-information game is a complete specification of which deterministic action to take at every node belonging to that player.
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