Game Theory_lecture6_08_handouts_1

Game Theory_lecture6_08_handouts_1 - EF4484-Game...

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EF4484--Game Theory--Lecture 6 10/22/2008 1 Dynamic Games of Complete Information Extensive-Form Representation Game Tree 10/22/2008 EF4484--Game Theory--Lecture 6 2 Outline of dynamic games of complete information Dynamic games of complete information Extensive-form representation Dynamic games of complete and perfect information Game tree Subgame-perfect Nash equilibrium Backward induction Applications Dynamic games of complete and imperfect information More applications Repeated games 10/22/2008 EF4484--Game Theory--Lecture 6 3 Today’s Agenda Examples Entry game Sequential-move matching pennies Extensive-form representation Dynamic games of complete and perfect information Game tree Mid-term Exam 4 Representations The two representations of the rules of a game are The normal (strategic) form The extensive form 10/22/2008 EF4484--Game Theory--Lecture 6
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10/22/2008 2 5 The Normal (Strategic) Form The normal form of a game is represented as a matrix or a table: Rows correspond to the strategies of player 1 and columns correspond to the strategies of player 2 . In each cell of the table , we write the payoffs associated with that pair of strategies. Player 2 c d Player 1 a 3 , 4 5 , 2 b 1 , 1 0 , 6 10/22/2008 EF4484--Game Theory--Lecture 6 6 The Extensive Form The extensive form is represented as a game tree . A game tree starts from a root : one of the players has to make a choice. The variable choices available to this player are represented as branches emanating from the root. At the end of each one of the branches that emerge from the root, it may split into further branches. The payoffs are written at the end of the tree where the game terminates. 10/22/2008 EF4484--Game Theory--Lecture 6 10/22/2008 EF4484--Game Theory--Lecture 6 7 Example: Entry game An incumbent monopolist faces the possibility of entry by a challenger . The challenger may choose to enter or stay out . If the challenger enters, the incumbent can choose either to accommodate or to fight . The payoffs are common knowledge. Challenger In Out Incumbent A F 1 , 2 2 , 1 0 , 0 The first number is the payoff of the challenger. The second number is the payoff of the incumbent. 10/22/2008 EF4484--Game Theory--Lecture 6 8 Example: Sequential matching pennies Each of the two players has a penny. Player 1 first chooses whether to show the Head or the Tail. After observing player 1’s choice, player 2 chooses to show Head or Tail Both players know the following rules: If two pennies match (both heads or both tails) then player 2 wins player 1’s penny. Otherwise, player 1 wins
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This note was uploaded on 02/22/2009 for the course ECONOMICS 4313 taught by Professor Tsui during the Spring '09 term at HKU.

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Game Theory_lecture6_08_handouts_1 - EF4484-Game...

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