Dynamic Games Flashcards
What is the extensive form - and how do you show static/dynaic complete/incomplete info games?
Dotted line = player 2 does not know which nod they are at – imperfect info / static game
What are the conditions for a game to be a subgame?
In games with complete and perfect info, a subgame is part of the game that:
has a single initial node
contains all the nodes that are successors of the single node
contains all the nodes that are successors of any node it contains
What is a proper subgame?
a sub game that is not the game itself
What is a sequential game?
Players move sequentiallyplayers have complete information
When do players have perfect info in a sequentail game?
Players have perfect info if at every time a player has to make a move, they know the full history of moves up until that point, before they make their choice.
Define a subgame perfect Nash equilibrium
All equilibrium strategy profiles are a Nash equilibrium in every subgame - eliminates non-credible threats
What are the methods of finding nash equilbia in sequentail games, describe each?
Backwards induction - Look at end nodes and work out best responses upwards - ensures subgame nash equilbria
Via subgames - Split game into subgames + find BR in each subgame - strategy that is best response in all is the subgame perfect Nash equilibrium
What is the equation for the pay-off of a repeated game when there is a discount?
What is a non-credible threat?
A threat, that if the player was forced to decide, they would be better off not doing, and choosing an alternative strategy.
Can you transform a repeated game termal history by an afine tranformation?
No, would sque the preferences, but can apply to each peroid individually and then re-work the game
How do you work out the equilibrium in a repeated game?
Find equilibrium using backwards induction by starting at the last game, and adding the outcome to the second to last, until you get to the first stage of the game - find Nash equilibrium
What is the equation for the terminal histroy of a reapeated game?
If stage game of a repeated game has a unqiue Nash equilibrium, what is the unqiue-perfect outcome?
The Nash equilibrium of G is played in every stage.
Show that (M’M’’, R’R’’) is a subgame perfect Nash equilbrium, and what does this prove?
The Nash equilibrium (L′,L′′) in Table (ii) corresponds with the subgame-perfect outcome ((L′, L′′) , (L′, L′′)). & the Nash equilibrium (R′,R′′) in Table (ii) corresponds with the subgame-perfect outcome ((R′, R′′) , (L′, L′′)).
The third Nash equilibrium in Table (ii), (M′,M′′), is different, however. It corresponds with the subgame-perfect outcome ((M′, M′′) , (R′, R′′)).
Thus, cooperation can be achieved in the first stage of a subgame-perfect outcome of the repeated game.
- this shows that subgame Nash perfect equilibrium does not ALWAYS rule out non-credible threats
What strategies can be used to enroucage cooperation in repeated games?
Threat of punishment:
- grim trigger (if you deviate, i will punish you forever)
- tit-for-tat (what you do this round ill do next round
