Term 2 week 5 Flashcards
What happens in a nash-equilibrium with a zero-sum and symmetric
The expected utility to each player in equilibrium is zero
How do you write the expected payoff when playing mixed strategy with equal p in RPS?
What are the propositions to prove a a NE in mixed strategy
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
In the variation of RPLS how does the game set out in a circle?
Action beats everything on the clockwise half circle of its anitposed
and is beaten by everything on the anti-clockwise half circle
For symetric non zero sum games with an odd number of actions what can be concluded?
How do we prove this?
That mixed strategy of equal probability can be found
Using osborne’s proposition
What is the difference between rock paper scissors well
How can you show the NE and show this is a NE and b unique
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
What is a real life application of RPSW
How do you prove that NE in RPS is unique
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
What is correlated equilibrium?
How do you compute the mixed strategy nash equilibrium payoff
What is another way of doing it?
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
What is a convex hole?
How does a coin toss impact the game of chicken?
What impact does this have on the convex hole
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
What are the correlated equilibrium random selection devices and what is the impact?
How do you calculate the expected payoff of such a situation
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
How do you solve static games of complete information
Using NE
