Game Theory

Question 1

Dominant strategy

Answer 1

When the player always chooses a certain strategy.

Question 2

Dominant strategy equilbrium

Answer 2

When both players choose their dominant strategy

Question 3

Nash equilibrium

Answer 3

Action is best response given the other players action.

Means no incentive to change action.

Question 4

Look at NE diagram for example

Question 5

Example where there is no NE

Answer 5

All 4 cells chosen with equal probability, so expected payoff of 0.5 for each player in this example

Question 6

So, no nash equilbrium is a mixed strategy equilibrium, what does this mean.

Answer 6

No player plays a given strategy with certainty

Question 7

Example of nash equilbrium not being the best outcome.

Answer 7

Both would be better off at deny deny, but not a nash equilibrium.

E.g if A denies, B would rather confess (since 0>-1). Same vice versa. So dominant strategy for both is to confess.

Question 8

How could they get to both deny

Answer 8

Coordinate (picture this in collusion - illegal!)

Question 9

Best response functions (2)

Answer 9

r* = r to the br (c*)

Is the row players best response to any choice by the column player.

c* = c to the br (r*)

Column players best response to any choice of the row player.

So r* and c* are best responses to each other, so no incentive to change their action.

Question 10

Sequential games

Answer 10

Now we will consider when choices are made in turns (rather than simultaneously, so 2nd player can observe actions of the first before making their choice.

E.g chess

Question 11

Example of sequential game.

Question 12

Put example in extensive form, and how can we find the equilbrium

Answer 12

Solve backwards with B’s choice.

Question 13

Repeated games - what do they allow

Answer 13

If same players interact repeatedly, they can learn from each others choices.

E.g they may learn to coordinate and both deny.