need help

[pliant gazelle]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[tender sable]

Ah the prisoner's dilemma!

If Beatrice goes for a hare, what does Alfonso get when going for a hare and what if he goes for the deer instead?

[final cove]

would it be that he should go for the deer?

that would be the best response right?

[tender sable]

Why would that be the best response?

[final cove]

because he would get the biggest portion

[tender sable]

Are you sure that's right?

[final cove]

i'm not dure

sure

[tender sable]

I suggest you read the question again

[final cove]

ok one sec

ok so

both going for deer = payoff of 10 each

one going deer and one hare = payoff of 0 and 3

and if both go for hare = payoff 3 each

what are payoff mean?

@tender sable

[tender sable]

Payoff is the reward expressed as a number, higher is better

[final cove]

oh I see

so he shouldn't go for the deer then

in that case, he should also go for the hare

[tender sable]

I agree!

[final cove]

but surely just me saying that isn't worth 13 marks right

[tender sable]

Can you explain in words why?

[final cove]

because he would be getting the highest payoff if he went with the hare in respct to the other option

[tender sable]

I don't think so, you'd need to provide an argument as to why this is the case

[tender sable]

Sounds good to me!

[final cove]

that's worth 13 marks?

[tender sable]

And what if he did not know what Beatrice would do?

That's the actual prisoner's dilemma

[final cove]

he should still go for the hare

[tender sable]

Hmmmmm why?

[final cove]

because choosing hare will always give a payoff of +3

whereas if he chooses deer

actually wait

that's a hard question

[tender sable]

Right? That's why it is a dilemma!

[final cove]

haha

what would you say for this?

[tender sable]

I know what the optimal strategy is in this case

In game theory your opponent is someone that always chooses the "best option"

[final cove]

ohhh so deer then

[tender sable]

In this case choosing the deer is beneficial to both you and the other person, whereas going for the hare is worse

The actual prisoner's dilemma is different

[final cove]

what is it?

here's another question too

not sure what nash equilibrium means

[tender sable]

Nash equilibrium is about the optimal choice of a player given that the other player chooses a certain option

So the question before was the nash equilibrium for Alfonso given that Beatrice chose the hare

[final cove]

ohh I see

so it's the same concept but different wording?

is the nash equilibrium 3?

[tender sable]

No the Nash equilibrium is the strategy you employ given that the other person does a certain strategy

Let's say that the other person goes for a hare. You would also go for a hare in that case, since it has the better payoff

If the other person goes for the deer you would also do so, since then the payoff is higher

[final cove]

so that would be 1 nash for this instance?

or do I not say how many in numbers but rather explain each strategy?

[tender sable]

Yes you say the strategy

I believe it is something like (hare,hare) and (deer,deer)? Not sure, I'd have to look that up

[final cove]

ok here are the strategies:

1. if one goes for deer, then it would be optimal to also go for deer as the payoff for each is 10

2. if one goes for hare, it would also be optimal to go for hare as the payoff for each is 3

3. if one goes for deer then it would be optimal to go for hare as they will get a payoff of 10.

[final cove]

ohh yes, now that you say that it rings a bell

1. (deer,deer)
   2.(deer,hare)
   3.(hare,hare)
   4.(hare,deer)

I hope that's correct

[tender sable]

Those are not the equilibria but all possible combinations of events

Because 2 and 4 don't seem to be equilibria

[final cove]

I see, how would I do it?

[tender sable]

The equilibria are, given that person A chooses option a, what would be the best to do for person B

[final cove]

I believe there are only two optimal startegies in this case

[tender sable]

I agree

[final cove]

(deer,deer) and (hare,hare)

[tender sable]

Exactly

[final cove]

thankyou, I already learned so much from you

this is the last one for part b

[final cove]

before that, so if I just say this, I get 13 marks?

or do I explain why too

[tender sable]

I think you'd have to explain why too

[final cove]

ok 👍

[final cove]

I'll be back in 5mins and we can do this one

if you want

ok im back

[final cove]

the respective payoff would be 10?

because in this case, they would both get the maximum desired benefit

[tender sable]

Because if you could communicate and would be bound to that that would be the best?

I find it curious that probability is not a factor in these questions

[final cove]

yes

so we answered all three?

[tender sable]

Wait I want to check something

[final cove]

ok

[tender sable]

The probability for the other player choosing each of the two options

Suppose that I chose to hunt the deer.
The expected payoff would be:
$10g+0(1-g)$
Where g is the probability that the other person goes for the deer.
Whereas the payoff when I'm going for the hare:
$3g+3(1-g)$

[lime willow]

Lumberdude #LeaveWolfAsHeIs

[final cove]

now im confused

[tender sable]

I'm sorry

[final cove]

would I need to do probabilities in my answers?

[tender sable]

Maybe for the optimal strategy, but that hasn't been a question.

[final cove]

true because I have doubts that they would give me 13 marks for each of those

it seems too easy

[tender sable]

Because the last question is not optimal strategy but strategy given that you can communicate

[tender sable]

Ok, the payoff for the hare here is 3, that seems right!

The payoff for the deer is 10 times the probability the other player goes for the deer too. That means that that strategy is optimal if the chance that the other player goes for the deer is bigger than 3/10

[tender sable]

Yeah idk how hard these are supposed to be?

[final cove]

they are for an undergraduate year 2 economics exam

it's a sample paper which replicates what the actual exam would be like

[tender sable]

Aaaah, can you discuss these with a TA or the lectrurer?

[final cove]

ok I'll send an email to see what they say

[final cove]

should I ask if it includes probabilities?

[tender sable]

Might be good to know for the actual exam maybe?

I dunno

[final cove]

yes, I'll ask

do you know how to solve these?

[final cove]

@tender sable

[tender sable]

I'm no economist

I will look it up

Ok it seems like it is described by dy/dx or dx/dy

[final cove]

yes

pretty much

[tender sable]

I think dy/dx

[final cove]

for number 1

ln(y) = 1/y right

[tender sable]

The derivative of U wrt y is 1/y, yes

[final cove]

ok

and x = 1?

[tender sable]

Yes

[final cove]

ok so now we divide x and y

so 1 divided by 1/y

which is the same as 1 multiplied by y/1

so 1*y = y

so the answer is D?

[tender sable]

Yes!

[final cove]

nice

[tender sable]

Well done dude

[final cove]

thankyou

now for number 2

first lets differentiate

and let me find x

so make y = 0

that would be:

-2x + 2

nvm i'm confused

so far I got:

u(x) = -2x + 2

[tender sable]

That's the du/dx?

[final cove]

I think so

i defo done something wrong

not sure

[tender sable]

I don't know how to go about that specific question haha

[final cove]

maybe if I -2

so it would be

2 = -2x

then divide by -2

so 2 divided by -2

= -1

so x would be -1?

[tender sable]

I know MRS, this I do not know man

Maybe ask in general if there are any economists around

[final cove]

will do 👍

[tender sable]

I will try reading into it

[final cove]

do you know about quantitative economics

[tender sable]

Unfortunately I do not

[final cove]

this for example

check it out - I found another variation to part B 😥

this one has probabilites

[final cove]

would the answer to number 1 be P + P?

[tender sable]

Hmm how did you get that answer?

[final cove]

ik it's wrong haha

[tender sable]

Try to work it out by summing the two probabilities*payoff

If you go for a deer, what is the chance that the other person goes for a deer, what is the chance that they go for a hare, what is the average value you get

[final cove]

im confused sorry]

[tender sable]

Ok I'll give you another example

Let's say I'm playing a game where I have to call heads or tails on a coin toss. If my choice wins I get $10, if I have it wrong I win nothing.
My expected payoff if I choose heads is:
p*10+(1-p)*0, where p= probability that the coin lands on heads

[final cove]

what does 1-p stand for?

and the 0

[tender sable]

The probability that it does not land on heads

0 is the payoff if it lands tails

[final cove]

I see

so P is heads

[tender sable]

In my example yes

[final cove]

1-P means not landing on heads

and 0 is tails

[tender sable]

Yes, since there are only two options

[final cove]

ok

and what shall I find?

[tender sable]

It is the payoff for tails, given that I'm going for heads

[final cove]

in this example

[final cove]

ohh

[tender sable]

It is the expected payout given that I chose heads

[final cove]

yes, makes sense

because you'll get nothing

if it doesn't land on heads

[final cove]

so in this case it would be:

P(10) + (1-P) * 0

that's the general equation?

so the expected payoff for Alonso going for deer

is P(10)?

or P(10) - (1-p)

[tender sable]

Yes exactly

No the probability for the other person going for the deer should be the same