Term 2 week 6

Question 1

What changes when a game is dynamic?

Answer 1

Players can act sequentially

Question 2

What types of game are assurance and battle and what type of games are these?

Answer 2

COordination game

In assurance you agree on the best outcome

IN battle you do not agree on the best outcome.

Question 3

What is the difference between normal and extensive form?

What does a dashed line connecting nodes mean?

Answer 3

1.Normal form = In payoff matrix
Extensive form = the nodes

2. It means they do not know where they are

Question 4

What is the difference between a singleton and non-singleton decision node?

Answer 4

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.

Question 5

What is the difference between complete information and perfect information

Answer 5

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

Question 6

How do you transfer a game from normal form to extensive form in imperfect information setting where extensive form is known

Answer 6

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.

Question 7

When finding NE how can eq be criticsied

Answer 7

It may not be rational in every sub game?

Question 8

What is sub-game perfect?

Answer 8

When the play is rational in every sub game

Question 9

How do you solve for perfect sub-game nash equilibria?

Answer 9

• Backward induction
  -See what the person would choose at each sub game to maximise payoffs

Question 10

When is a nash equilibrium said to be sub-game perfect game

Answer 10

If the player is taking an optimal strategy at every sub-game.

Question 11

How do you count how many sub-games there are in a game?

How are they called differently?

Answer 11

The whole game is one
Then the subgames starting at the other nodes.

Question 12

What is the benefit of sub-game perfection?

Answer 12

It eliminates not credible threats

Question 13

What is a proper sub game

Answer 13

Not the whole game but the smaller sub games.

Question 14

Try presenting a game in normal form with 3 players.

Question 15

Why when there are two sub games must you always put two actions like LR?

Answer 15

Because they must have a plan of action at each node, even if they dont end up doing it.

Question 16

What should be considered in repeated game?

Answer 16

That you should discount the future payoff
{0,1}
The closer to 1 the more they care about the future.

Question 17

What is a rule for repeated games?

(Stage games)

When does this only happen?

Answer 17

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!

Question 18

What is the shortcoming of sub-game perfect nash equilbria

Why is this?

Answer 18

• 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.

Question 19

What happens in repeated games if there is no unique NE?

Answer 19

If there is no unique NE it is possible that in a penultimate game something

Question 20

What are the possible infinite cooperation strategies?

Question 21

How do you calculate the payoff in infinite game?

Answer 21

You do a/ 1-r
r is the ratio between time periods

Question 22

How do you calculate when you would do the strategy?

Answer 22

You compare the present discounted value of each strategy and see what discount rate is needed.