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1

What are repeated games?

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

2

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

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

3

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

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!

4

What is a grim trigger strategy?

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.

5

What's a Disadvantage of the grim trigger strategy?

A single mistake by a player causes a disastrous outcome.

6

How can grim trigger help in solving prisoners' dilemmas?

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.

7

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

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).”

8

How can you solve ∞Σₜ₌₁ 𝛿ᵗ⁻¹ X ?

1/(1-𝛿) X

9

How do folk theorems help to solve infinitely repeated games?

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

10

What is a stationary strategy?

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

11

What defines Rubenstein bargaining?

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