Game Theory_lecture8_08_handouts

Game Theory_lecture8_08_handouts - EF4484-Game...

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EF4484-Game Theory-Lecture 8 11/5/08 1 1 Dynamic Games of Complete Information Dynamic Games of Complete and Perfect Information 11/5/08 EF4484-Game Theory-Lecture 8 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 11/5/08 EF4484-Game Theory-Lecture 8 3 Today’s Agenda Exercise Review of previous class Subgame-perfect Nash equilibrium Backward induction Stackelberg’s model of duopoly Sequential-move Bertrand model of duopoly 11/5/08 EF4484-Game Theory-Lecture 8 4 Dynamic games of complete and perfect information Perfect information All previous moves are observed before the next move is chosen. A player knows Who has moved What before she makes a decision 11/5/08 EF4484-Game Theory-Lecture 8
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EF4484-Game Theory-Lecture 8 11/5/08 2 5 Nash equilibrium in a dynamic game We can also use normal-form to represent a dynamic game The set of Nash equilibria in a dynamic game of complete information is the set of Nash equilibria of its normal-form How to find the Nash equilibria in a dynamic game of complete information Construct the normal-form of the dynamic game of complete information Find the Nash equilibria in the normal-form 11/5/08 EF4484-Game Theory-Lecture 8 6 Subgame-perfect Nash equilibrium A Nash equilibrium of a dynamic game is subgame-perfect if the strategies of the Nash equilibrium constitute or induce a Nash equilibrium in every subgame of the game. Subgame-perfect Nash equilibrium is a Nash equilibrium. 11/5/08 EF4484-Game Theory-Lecture 8 7 Subgame A subgame of a game tree begins at a nonterminal node and includes all the nodes and branches following the nonterminal node A subgame beginning at a nonterminal node x can be obtained as follows: remove the branch connecting x and its predecessor the connected part containing x is the subgame -1 , 1 Player 1 Player 2 H T 1 , -1 H T Player 2 H T 1 , -1 -1 , 1 a subgame 11/5/08 EF4484-Game Theory-Lecture 8 8 Existence of subgame-perfect Nash equilibrium Every finite dynamic game of complete and perfect information has a subgame-perfect Nash equilibrium (that can be found by backward induction*). * see the previous slides for limitations of backward induction 11/5/08 EF4484-Game Theory-Lecture 8
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EF4484-Game Theory-Lecture 8 11/5/08 3 Experiment: Game of 23 and 7 Your data 1 st played the Game of 23 3, 21.4% 0, 0% 2, 14.4% 5, 35.6% 3, 21.4% 1, 7.2% 2 nd played the Game of 7 14, 87.5% 4, 25% 1, 6.25% 2, 12.5% 5, 31.25% 2, 12.5% 2, 12.5% 2, 12.5% 3 rd played the Game of 23 11/5/08 9 EF4484-Game Theory-Lecture 8 Epiphany in the Game of 21 Dufwenberg, Sundaram, and Butler (2008) 11/5/08 EF4484-Game Theory-Lecture 8 10 Epiphany in the Game of 21 Dufwenberg, Sundaram, and Butler (2008) 11/5/08 EF4484-Game Theory-Lecture 8 11 Epiphany in the Game of 21 Dufwenberg, Sundaram, and Butler (2008) 11/5/08 EF4484-Game Theory-Lecture 8 12
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