Game Theory_lecture7_08_handouts

Game Theory_lecture7_08_handouts - EF4484-Game...

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EF4484--Game Theory--Lecture 7 10/29/2008 1 Dynamic Games of Complete Information Extensive-Form Representation Game Tree 10/29/08 EF4484--Game Theory--Lecture 7 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 10/29/08 EF4484--Game Theory--Lecture 7 3 Today’s Agenda Review of previous class Subgame Subgame-perfect Nash equilibrium Backward induction 10/29/08 EF4484--Game Theory--Lecture 7 4 Dynamic (or sequential-move) games of complete information A set of players Who moves when and what action choices are available? What do players know when they move? Players’ payoffs are determined by their choices. All these are common knowledge among the players.
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EF4484--Game Theory--Lecture 7 10/29/2008 2 10/29/08 EF4484--Game Theory--Lecture 7 5 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 10/29/08 EF4484--Game Theory--Lecture 7 6 Game tree A game tree has a set of nodes and a set of branches such that each branch connects two nodes (these two nodes are said to be adjacent ) for any pair of nodes, there is a unique path that connects these two nodes x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 a node A branch connecting nodes x 1 and x 5 a path from x 0 to x 4 10/29/08 EF4484--Game Theory--Lecture 7 7 Game tree Any node other than a terminal node represents some player. For a node other than a terminal node, the branches that connect it with its successors represent the actions available to the player represented by the node Player 1 Player 2 H T -1 , 1 1 , -1 H T Player 2 H T 1 , -1 -1 , 1 10/29/08 EF4484--Game Theory--Lecture 7 8 Game tree A path from the root to a terminal node represents a complete sequence of moves which determines the payoff at the terminal node Player 1 Player 2 H T -1 , 1 1 , -1 H T Player 2 H T 1 , -1 -1 , 1
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EF4484--Game Theory--Lecture 7 10/29/2008 3 10/29/08 EF4484--Game Theory--Lecture 7 9 Strategy and payoff A strategy for a player is a complete plan of actions. It specifies a feasible action for the player in every contingency in which the player might be called on to act. It specifies what the player does at each of her nodes Player 1 Player 2 H T -1 , 1 1 , -1 H T Player 2 H T 1 , -1 -1 , 1 a strategy for player 1: H a strategy for player 2: H if player 1 plays H , T if player 1 plays T (written as HT ) If player 1 plays H and player 2 plays HT, Player 1’s payoff is -1 and player 2’s payoff is 1 10 Suppose H-P is debating whether or not to enter a new market, where the market is dominated by its rival, Dell.
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