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##### Activity
• May 21 2017 10:33

drvinceknight on gh-pages

Fix typo. (compare)

• May 21 2017 10:29

drvinceknight on gh-pages

Fix typo. (compare)

• May 20 2017 17:49

drvinceknight on gh-pages

Correct typo on Ch 18. (compare)

• May 20 2017 17:43

drvinceknight on gh-pages

Fix errors in CH17. (compare)

• May 18 2017 10:58

drvinceknight on gh-pages

Fix typo in proof. (compare)

• May 17 2017 18:23

drvinceknight on gh-pages

Correct typo in solutions to hw. (compare)

• May 17 2017 17:59

drvinceknight on gh-pages

Correct feasible flow def heade… (compare)

• May 16 2017 10:32

drvinceknight on gh-pages

Fix a typo in hw 2 sol Merge branch 'gh-pages' of gith… (compare)

• May 08 2017 14:20

drvinceknight on gh-pages

s to c Merge pull request #2 from timo… (compare)

• May 08 2017 14:20
drvinceknight closed #2
• May 08 2017 14:20
drvinceknight commented #2
• May 08 2017 14:19

drvinceknight on gh-pages

Typo normal to extensive. Merge pull request #3 from Niko… (compare)

• May 08 2017 14:19
drvinceknight closed #3
• May 08 2017 12:28
Nikoleta-v3 opened #3
• Apr 25 2017 13:46

drvinceknight on gh-pages

Fix typo in Ch 11. (compare)

• Apr 04 2017 08:45

drvinceknight on gh-pages

Clarify sentence in HW5q2 solut… (compare)

• Mar 22 2017 07:39

drvinceknight on gh-pages

• Feb 26 2017 19:48

drvinceknight on gh-pages

Fix another typo in def of mixe… (compare)

• Feb 16 2017 16:41

drvinceknight on gh-pages

Correct solutions. (compare)

• Feb 16 2017 14:44

drvinceknight on gh-pages

Syntax fix to lesson plans. Add feedback feedback for 2016-… (compare)

Vince Knight
@drvinceknight
So you’re simply asked to follow the definition of a normal form game and use that to describe the situatin.
Where it says:
A $N$ player normal form game consists of: ...
Hope that helps.
@Huaraz2
think so,
Vince Knight
@drvinceknight
Hi all, here’s a video showing the basics of computing Nash equilibria for 2 by 2 games.
I’m doing this as an experiment with a new tool, if it’s helpful I can actually get these out pretty easily. Let me know if they’re helpful or not.
@Huaraz2
hey @drvinceknight I am doing HW1 and I don't quite understand how you get $B_2$ for Q5. I have that that player one uses the stratergy: $\sigma_2 = (x,y,1-x-y)$ and the resultent payoffs are: $U_2(\sigma_2, c_1) = 3x - y$ and $U_2(\sigma_2,c_2) = 2 - y$. Now looking at the answers I see that you say: $U_2(\sigma_2, c_1) > U_2(\sigma_2, c_2)$ but I can't see how this is obvious. Any help would be great thanks
Vince Knight
@drvinceknight
I don't say that, I look for values of x and y for which it's true.
Just trying to find values for which c1 is a br and similarly c2.
@Huaraz2
@drvinceknight are you using proof by contradiction to prove the equality of payoffs theorem for |S (sigma_i)| > 1 ?
Vince Knight
@drvinceknight
Yes.
@Huaraz2
:+1:
@Huaraz2
@drvinceknight we have to do stuff wrt infinitely repeated games, will the normal form game be similar to the prisoner's dilemma?
Vince Knight
@drvinceknight
I can't say. Potentially.
@Huaraz2
So can any normal form game be set as an infinitely repeated game then but the principles of how to deal with IFGs that we learnt wrt the prisoner's' dilemma are the same?
Vince Knight
@drvinceknight
Yup.
@Huaraz2
I know this is probably a really dull question
thanks Vince
Vince Knight
@drvinceknight
Don't worry about whether or not the question is dull.
I'm happy to help.
:)
@Huaraz2
YAY :smiling_imp:
Vince Knight
@drvinceknight
:+1:
@Huaraz2
:shipit:
@Huaraz2
@drvinceknight in the above pic you have the utility of both players players playing the strategy $S_c$ is $\frac{2}{1 - \delta}$. Is the 2 there because of the fact that the payoff for each player is 2?
Vince Knight
@drvinceknight
So that question is EXACTLY the same as in the notes.
@Huaraz2
I thought it was I was just checking
Vince Knight
@drvinceknight
Only difference is that players minimize as opposed to optimise.
So yeah they get 2 at each repetitions. When you apply discounting and use the formula for a geometric series you get that.
Heading off now but will be around tomorrow if there's anything else I can help with.
😴
@Huaraz2
night night @drvinceknight
@Huaraz2
@drvinceknight when looking at the transition probabilities for stochastic games am I right in assuming that the first number is the prob of staying in that game and the second is the prob of moving on to the next?
Vince Knight
@drvinceknight
Yes.
@Huaraz2
cool and also if all of the boxes connected does that mean that they are different strategies for the same game?
@Huaraz2
@drvinceknight in your notes you have a stochastic game where one of the states has a payoff of (0,0) and a transition probability of (0,1) which as far as I understand it would mean that players would definitely move on from this game once they have played it once. Why is it then that you refer to it as an absorbing state?
Vince Knight
@drvinceknight
In the notes the game that has a payoff of (0,0) is the second game.
So the transitions (0,1) mean that you always go to the second game (which is the same game). So once you’re there you’re absorbed.

is the prob of staying in that game and the second is the prob of moving on to the next?

Sorry, I scanned: that’s not correct.

If $\pi$ is the transition vector: $\pi_i$ is the probability of transitioning to game (i).
@Huaraz2
oh right so if there were three games then the transition probability vector would have three parts?
Vince Knight
@drvinceknight
Yup.
So (0,1) just means you always go to the second game.