Term 2 week 5

Question 1

What happens in a nash-equilibrium with a zero-sum and symmetric

Answer 1

The expected utility to each player in equilibrium is zero

Question 2

How do you write the expected payoff when playing mixed strategy with equal p in RPS?

Question 3

What are the propositions to prove a a NE in mixed strategy

Answer 3

1a if you deviate to one pure strategy within the mix you get 0 pure vs mixed

1b if you use a pure strategy outside the mix you get negative or 0 payoff

Question 4

In the variation of RPLS how does the game set out in a circle?

Answer 4

Action beats everything on the clockwise half circle of its anitposed
and is beaten by everything on the anti-clockwise half circle

Question 5

For symetric non zero sum games with an odd number of actions what can be concluded?

How do we prove this?

Answer 5

That mixed strategy of equal probability can be found

Using osborne’s proposition

Question 6

What is the difference between rock paper scissors well

How can you show the NE and show this is a NE and b unique

Answer 6

Well and paper beat two actions
Rock and scissors only beat one

Propose NE mixed strategy of playing
everything with equal probability but rock

Show that responding to a mixed with a pure all these payoffs are equaled to zero = osborne 1a

Then show that if you play the pure outside the mix against the mix you do not get a positive payoff

Question 7

What is a real life application of RPSW

Question 8

How do you prove that NE in RPS is unique

Answer 8

Prove by contradicition

Show what happens if you play adjacent actions with higher probability

Then show this can be exploited for positive payoff

which contradicts osbornes

Question 9

What is correlated equilibrium?

Question 10

How do you compute the mixed strategy nash equilibrium payoff

What is another way of doing it?

Answer 10

Once you have the NE probabilities
you then times the probabilities of being in each cell

Then you times this probability for player 1 payoff and player 2 payoff

Play a pure strategy against the mix

Question 11

What is a convex hole?

Question 12

How does a coin toss impact the game of chicken?

What impact does this have on the convex hole

Answer 12

There is no incentive to deviate and you also trust the umpire

Due to the pre lay arragnement

It allows them to get on a further point from the convex hole

Question 13

What are the correlated equilibrium random selection devices and what is the impact?

How do you calculate the expected payoff of such a situation

Answer 13

The probability in each cell is the probability with which the umpire chooses that cell and

you times payoff of that cell times by chance of being in that cell

Question 14

How do you solve static games of complete information

Answer 14

Using NE