Term 2 week 6 Flashcards
What changes when a game is dynamic?
Players can act sequentially
What types of game are assurance and battle and what type of games are these?
COordination game
In assurance you agree on the best outcome
IN battle you do not agree on the best outcome.
What is the difference between normal and extensive form?
What does a dashed line connecting nodes mean?
1.Normal form = In payoff matrix
Extensive form = the nodes
- It means they do not know where they are
What is the difference between a singleton and non-singleton decision node?
Non-singleton is connected by dashed line could connect three nodes for example
If a decision node is not connected by dashed line it is non-singleton.
What is the difference between complete information and perfect information
Complete information is when you know the extensive form
imperfect information is when you don’t know which side of the extensive form you are on
How do you transfer a game from normal form to extensive form in imperfect information setting where extensive form is known
The first player is easy as they can do U or D only
But player two must have a plan on both sides
So they can play LL RR LR and RL
As a result when putting it into normal form you need to put that in the table and then investigate the payoffs.
When finding NE how can eq be criticsied
It may not be rational in every sub game?
What is sub-game perfect?
When the play is rational in every sub game
How do you solve for perfect sub-game nash equilibria?
- Backward induction
-See what the person would choose at each sub game to maximise payoffs
When is a nash equilibrium said to be sub-game perfect game
If the player is taking an optimal strategy at every sub-game.
How do you count how many sub-games there are in a game?
How are they called differently?
The whole game is one
Then the subgames starting at the other nodes.
What is the benefit of sub-game perfection?
It eliminates not credible threats
What is a proper sub game
Not the whole game but the smaller sub games.
Try presenting a game in normal form with 3 players.
Why when there are two sub games must you always put two actions like LR?
Because they must have a plan of action at each node, even if they dont end up doing it.
What should be considered in repeated game?
That you should discount the future payoff
{0,1}
The closer to 1 the more they care about the future.
What is a rule for repeated games?
(Stage games)
When does this only happen?
if the stage game G has a unique equilibrium, then for finite T, the repeated game G(T) has a unique sub-game perfect outcome:
The unique NE is played in every stage.
NE must be unique!
What is the shortcoming of sub-game perfect nash equilbria
Why is this?
- It does not remove all non-credbile threats like someone reducing their own payoff to punish another person
-Not renegotiation proof
-Because even if you go against someone in the first period, you could negotitate with them to still get the better outcome for them.
What happens in repeated games if there is no unique NE?
If there is no unique NE it is possible that in a penultimate game something
What are the possible infinite cooperation strategies?
How do you calculate the payoff in infinite game?
You do a/ 1-r
r is the ratio between time periods
How do you calculate when you would do the strategy?
You compare the present discounted value of each strategy and see what discount rate is needed.
