Repeated and infinite games Flashcards
When does the strategy of choosing to co-operate in response to a grim trigger strategy become a best response?
When the discount rate is high enough - i.e we are sufficiently patient
What does subgame perfect NE require?
That strategies be optimal after EVERY possible history not just the ones that are reached if players adhere to their strategies
What is a credible threat of punishment? What has this got to do with SPNE?
A credible threat of punishment - implies that in a grim trigger/ limited punishment strategy (or whatever) you have to have an incentive to punish the other player. SPNE eliminates incredible threats
A strategy pair is a SPNE in a finite horizon game and infinite game iff…?
It satisfies the one-deviation property
State the one deviation property for the finite horizon game
no player can increase their payoff by changing her action at the start of any subgame in which she is the first-mover, given the other players’ strategies and the rest of her own strategy
State the one deviation property for the infinite game. How do we rationalise this for the infinite game?
no player can increase their payoff by changing their action at the beginning of a subgame in which they are the first mover, given the others’ strategies and given the rest of her own strategy
Past some arbitrarily large T, different strategies yield v similar, v small payoffs. Can still work back from T to obtain SPNE
In repeated games, what is the ‘form’ of the Nash equilibria?
a set of optimal strategies
How can we stop ordinal variations of a strategic game payoffs affecting preferences in the repeated game (whilst cardinality is held intact) ?
Monotonic transformations of the utility function to create IDENTICAL preferences in the repeated game
What is a history?
A sequence of action profiles in a game
What is a strategy?
a strategy specifies a player’s action for ALL POSSIBLE HISTORIES, even histories inconsistent with her strategy
Why is co-operation fundamentally not a possible SPNE in a finitely-repeated Prisoner’s Dilemma game?
In the last period, if you choose to defect, will not be punished. So your discounted ave. payoff will be at least as large as if you stuck to co-operating in all periods -> hence you deviate. This applies in all prior periods.
**Why is the ordinary grim trigger strategy pair NOT an SPNE of the infinite game for ANY value of the discount rate?
What is the Folk Theorem?:
In the limit as the discount rate tends to 1, a payoff vector can be obtained in an NE iff it is feasible and all players receive more than the minmax payoffs.
what is the set of feasible payoffs?
the set of all weighted averages of payoff profiles in the strategic game
What happens to the set of discounted average payoff profiles as the discount rate tends to 1?
They become approximately equal to the set of feasible payoff profiles in the component STRATEGIC game
