game below, hich is infinitely repeated at Both players discoun the future at rate ô € (0, 1). The stage game is C D C 5,5 |0,6 D 6,0 | 1,1 1. The following three questions are about “Grim Trigger" strategies. (a) Describe the “Grim Trigger" strategy profile of this game. (b) Draw the finite automata representation of this strategy profile. (c) Find the lowest value of 6 for this strategy profile to form a subgame perfec equilibrium. 2. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in perio t = 2,4, 6, ... Compute the discounted payoff of each player.
game below, hich is infinitely repeated at Both players discoun the future at rate ô € (0, 1). The stage game is C D C 5,5 |0,6 D 6,0 | 1,1 1. The following three questions are about “Grim Trigger" strategies. (a) Describe the “Grim Trigger" strategy profile of this game. (b) Draw the finite automata representation of this strategy profile. (c) Find the lowest value of 6 for this strategy profile to form a subgame perfec equilibrium. 2. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in perio t = 2,4, 6, ... Compute the discounted payoff of each player.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the game below, which is infinitely repeated at t = 1,2, . Both players discount
the future at rate d E (0, 1). The stage game is
C
D
C 5,5 0,6
D 6,0 1,1
1. The following three questions are about "Grim Trigger" strategies.
(a) Describe the "Grim Trigger" strategy profile of this game.
(b) Draw the finite automata representation of this strategy profile.
(c) Find the lowest value of d for this strategy profile to form a subgame perfect
equilibrium.
2. Suppose that the players play (C,C) in period t = 1,3, 5, ... and plays (D,D) in period
t = 2,4, 6, ... Compute the discounted payoff of each player.
3. Find a subgame perfect equilibrium such that, on the equilibrium path, (D,D) is played
at periods t = 1,3, 5 .., and (C,C) is played at periods t = 2, 4, 6, ... Write down the
finite automata representation for the strategy profile you proposed. Find the lowest
value of ő for the profile to form a subgame perfect equilibrium.
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