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1、June 11, 2003,73-347 Game Theory-Lecture 16,1,Dynamic Games of Complete Information,Dynamic Games of Complete and Imperfect Information,June 11, 2003,73-347 Game Theory-Lecture 16,2,Outline of dynamic games of complete information,Dynamic games of complete information Extensive-form representation D
2、ynamic 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,June 11, 2003,73-347 Game Theory-Lecture 16,3,Todays Agenda,Review of previous class Game t
3、ree representing imperfect information Subgame Subgame-perfect Nash equilibrium Backward induction,June 11, 2003,73-347 Game Theory-Lecture 16,4,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
4、 they move? Players payoffs are determined by their choices. All these are common knowledge among the players.,June 11, 2003,73-347 Game Theory-Lecture 16,5,Definition: extensive-form representation,The extensive-form representation of a game specifies: the players in the game when each player has t
5、he move what each player can do at each of his or her opportunities to move what each player knows at each of his or her opportunities to move the payoff received by each player for each combination of moves that could be chosen by the players,June 11, 2003,73-347 Game Theory-Lecture 16,6,Dynamic ga
6、mes of complete and perfect information,Perfect information All previous moves are observed before the next move is chosen. A player knows Who has made What choices when she has an opportunity to make a choice,June 11, 2003,73-347 Game Theory-Lecture 16,7,Perfect information: illustration (sequentia
7、l 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 1s 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 play
8、er 1s penny. Otherwise, player 1 wins player 2s penny.,Player 1,Player 2,H,T,-1, 1,1, -1,H,T,Player 2,H,T,1, -1,-1, 1,June 11, 2003,73-347 Game Theory-Lecture 16,8,Dynamic games of complete and imperfect information,Imperfect information A player may not know exactly Who has made What choices when s
9、he has an opportunity to make a choice. Example: player 2 makes her choice after player 1 does. Player 2 needs to make her decision without knowing what player 1 has made.,June 11, 2003,73-347 Game Theory-Lecture 16,9,Imperfect information: illustration,Each of the two players has a penny. Player 1
10、first chooses whether to show the Head or the Tail. Then player 2 chooses to show Head or Tail without knowing player 1s choice, Both players know the following rules: If two pennies match (both heads or both tails) then player 2 wins player 1s penny. Otherwise, player 1 wins player 2s penny.,Player
11、 2,June 11, 2003,73-347 Game Theory-Lecture 16,10,Information set,Gibbons definition: An information set for a player is a collection of nodes satisfying: the player has the move at every node in the information set, and when the play of the game reaches a node in the information set, the player wit
12、h the move does not know which node in the information set has (or has not) been reached. All the nodes in an information set belong to the same player The player must have the same set of feasible actions at each node in the information set.,June 11, 2003,73-347 Game Theory-Lecture 16,11,Informatio
13、n set: illustration,an information set for player 3 containing three nodes,an information set for player 3 containing a single node,two information sets for player 2 each containing a single node,June 11, 2003,73-347 Game Theory-Lecture 16,12,Information set: illustration,All the nodes in an informa
14、tion set belong to the same player,Player 1,C,D,Player 2,E,F,3, 0, 2,2, 1, 3,Player 3,G,H,1, 3, 1,0, 2, 2,This is not a correct information set,June 11, 2003,73-347 Game Theory-Lecture 16,13,Information set: illustration,The player must have the same set of feasible actions at each node in the infor
15、mation set.,Player 1,C,D,Player 2,E,F,3, 0,2, 1,Player 2,G,H,1, 3,0, 2,1, 1,An information set cannot contains these two nodes,K,June 11, 2003,73-347 Game Theory-Lecture 16,14,Represent a static game as a game tree: illustration,Prisoners dilemma (another representation of the game in Figure 2.4.3 o
16、f Gibbons. The first number is the payoff for player 1, and the second number is the payoff for player 2),June 11, 2003,73-347 Game Theory-Lecture 16,15,Example: mutually assured destruction,Two superpowers, 1 and 2, have engaged in a provocative incident. The timing is as follows. The game starts with superpower 1s choice either ignore the incident ( I ), resulting in the payoffs (0, 0), or to escalate the situatio
