Flashcards in 06 - Dynamic Games of Complete Information Deck (11)
What are repeated games?
A game G which is a static game, but is repeated in t periods
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
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!
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.
What's a Disadvantage of the grim trigger strategy?
A single mistake by a player causes a disastrous outcome.
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.
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).”
How can you solve ∞Σₜ₌₁ 𝛿ᵗ⁻¹ X ?
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
What is a stationary strategy?
Strategies stay the same, as all odd and all even periods are exactly the same