LECTURE 3 DYNAMIC GAMES OF COMPLETE INFORMATION Notes modified from Yongqin Wang@ Fudan University
LECTURE 3 DYNAMIC GAMES OF COMPLETE INFORMATION Notes modified from Yongqin Wang @ Fudan University
Outline of dynamic games of complete information Dynamic games of complete information EXtensive-form representation Dynamic games of complete and perfect information ■ Game tree a Subgame-perfect Nash equilibrium Backward induction Applications Dynamic games of complete and imperfect information ■ More applications Repeated games
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 2
Entry game a An incumbent monopolist faces the possibility of entry by a challenger The challenger may choose to enter or stay out a If the challenger enters the incumbent can choose either to accommodate or to fight The payoffs are common knowledge Challenger Incumbent The first number is the A payoff of the challenger The second number is the payoff of the incumbent 2,1 0,0
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. 3 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
Sequential-move matching pennies Player Each of the two players has a penny Player 1 first chooses H Whether to show the head or the tail Player 2 Player 2 After observing player 1's choice, player 2 chooses to show head or tail H T H T 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 2's penny
Sequential-move 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 player 2’s penny. 4 Player 1 Player 2 H T -1, 1 1, -1 H T Player 2 H T 1, -1 -1, 1
Dynamic(or sequential-move) games of complete information a set of players Who moves when and what action choices are available? a What do players know when they move? a Players payoffs are determined by their choices All these are common knowledge among the players
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. 5