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ECON 2350 Lecture Notes - Lecture 17: Nash Equilibrium, Subgame

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School
York University
Department
Economics
Course
ECON 2350
Professor
Ying Kong

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Document Summary

Here is the one-period version of it that we considered before. u suppose that this game will be played in each of only 3 periods; t = 1, What is the likely outcome? u suppose the start of period t = 3 has been reached (i. e. the game has already been played twice). Bonnie do? u suppose the start of period t = 3 has been reached (i. e. the game has already been played twice). Both should choose confess. u now suppose the start of period t = 2 has been reached. What should bonnie do? u now suppose the start of period t = 2 has been reached. Bonnie expect each will choose confess next period. Both should choose confess. u at the start of period t = 1 clyde and bonnie both expect that each will choose confess in each of the next two periods.

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Related Questions

Consider the following game. Player 1 has an infinite set of pure strategies, which is the interval [0, 1]. Player 2 has only two pure strategies, L and R. When Player 1 chooses his pure strategy x ∈ [0, 1], payoffs to Player 1 are u1(x, L) = 2 − 2x, u1(x, R) = x; and payoffs to Player 2 are u2(x, L) = x, u2(x, R) = 1 − x.

(i) Show that the game has no Nash equilibrium in pure strategies.

(ii) Find all Nash equilibria of the game when Player 2 is allowed to use a mixed strategy. Explain carefully why they are Nash equilibria. Give the payoffs to the two players.

<p>Suppose two people are playing a game (Bill and Amanda). Each player has two possible actions: Left; and<br />Right. The payos are reported in the table below; the rst number is Amanda's payo and the second is<br />Bill's.<br />Bill<br />Left Right<br />Amanda Left 6,6 11,2<br />Right 2,11 9,9<br />a) What is the pure strategy Nash equilibrium of this game?<br /><br />Now suppose this game is played twice, once today and once tomorrow (repeated prisoners' dilemma).Further, suppose that because of discounting, a payoff tomorrow of X, is only worth (.9)X today.<br />b) What is Amanda's payoff when both players play the Nash equilibrium on both days?<br /><br />Suppose Bill makes the following credible claim "I will play "Right" on each day. However, if on the first day I play "Right" and Amanda plays "Left," I will play "Left" for the rest of time."<br />c) What is Amanda's payoff if she plays "Right" on both days.<br />d) What is Amanda's payoff if she plays "Left" on the first day and plays "Right" on the second day?<br />e) What is Amanda's optimal strategy?</p>
  • Consider the infinitely repeated game of Prisoners Dilemma that has the following payoff structure. Each player has a discount rate r. Suppose both players are using the Tit-For-Tat strategy.

 

Column

 

Defect   

Cooperate

Row

Defect

2, 2

10, 1

Cooperate

1, 10

6, 6

 

  • (a) Under what condition does a player have an incentive to deviate once from cooperating and then revert to it? [4 points]
  • (b) Under what condition does a player have an incentive to deviate from cooperating forever? [4 points]
  • (c) Under what condition is it a Nash equilibrium that both players use the Tit-For-Tat strategy? [2 points]