06 - Dynamic Games of Complete Information

Question 1

What are repeated games?

Answer 1

A game G which is a static game, but is repeated in t periods

Question 2

How can you solve a repeated game with a unique Nash Equilibrium?

Answer 2

If the stage game G has a unique Nash equilibrium a = (a1, …, an), then, for any finite T, the repeated game G(T) has a unique subgame perfect Nash equilibrium: each player i plays ai in every stage after any history up to that stage.

Proof: Backwards induction: N.E. will be played in the last phase. add it to all payoffs. N.E. will also be played in the period before! etc etc

Question 3

How can you solve a repeated game with multiple Nash Equilibrium?

Answer 3

Use N.E. from last phase to make credible threats in phase before -> add payoffs to first phase and observe true SPNE, based on cooperation!

Question 4

What is a grim trigger strategy?

Answer 4

Grim trigger is a trigger strategy for a repeated game. Initially, a player using grim trigger will cooperate, but as soon as the opponent defects, the player using grim trigger will defect for the remainder of the iterated game.

Question 5

What’s a Disadvantage of the grim trigger strategy?

Answer 5

A single mistake by a player causes a disastrous outcome.

Question 6

How can grim trigger help in solving prisoners’ dilemmas?

Answer 6

The grim trigger strategy achieves cooperation in the Prisoner’s Dilemma through the credible threat of punishing a deviation forever. This threat works if players care enough about the future.

Question 7

How could cooperation be achieved with less drastic punishment than grim-trigger?

Answer 7

For example, using the perfect tit-for-tat strategy:
Example prisoner’s dilemma: “Play Ri in stage 1. Play Ri in stage t if the outcome of stage t − 1 was either (R1,R2) or (L1,L2). Play Li in stage t if the outcome of stage t − 1 has been either (L1,R2) or (R1,L2).”

Question 8

How can you solve ∞Σₜ₌₁ 𝛿ᵗ⁻¹ X ?

Answer 8

1/(1-𝛿) X

Question 9

How do folk theorems help to solve infinitely repeated games?

Answer 9

Use the term (1-𝛿) for finding the average value of discounting: (1-𝛿) ∞Σₜ₌₁ 𝛿ᵗ⁻¹ X = X

Question 10

What is a stationary strategy?

Answer 10

Strategies stay the same, as all odd and all even periods are exactly the same

Question 11

What defines Rubenstein bargaining?

Answer 11

• back-and-forth-bargaining
• no arbitrary cutoff point
• neither player knows who will make the last offer.