game theory?

[LimpyLoo]

mcbpete? more like..................

 

......

 

 

 

......

 

.....

 

......

 

.....

 

 

[bah, i can't think of anything clever...sorry]

 

[triachus]

mcbpete? more like..................

 

......

 

 

 

......

 

.....

 

......

 

.....

 

MC BEE PETE

 

 

or like .............·.

 

DJ PETE BEE

 

https://soundcloud.com/dj-pete-bee

fixt

[chenGOD]

 

 

 

 

 

let's see if i can remember:

 

 

 

Firm B's output will be on the left and firm A's output will be on the right in each quadrant (since I can't do tables in the board there will be no lines, so hopefully this is clear)

 

FIRM A's OUTPUT

One-half Two-Thirds

Monopoly Monopoly

Profit Profit

 

F O One-half

I U Monopoly 20|20 15|22

R T Profit

M P

U

B' T Two-thirds

s Monopoly 22|15 17|17

Profit

 

 

Where's the Nash Equilibrium? Explain your answer, and what are the implications of a Nash equilibrium?

So, a Nash equilibrium occurs when players can no longer exploit each other. The behavior of both players will 'settle' into a Nash equilibrium.

 

Here, there is a question as to whether the two firms can comminucate beforehand, and whether there are meta-game reasons not to cooperate. But if the firms are especially unfriendly they"ll just go in circles trying to exploit each other. And since there is no way to avoid being exploited...

 

Bah I just woke up to piss and now I'm trying to solve game theory puzzles. Alright lemme think here...

 

Okay, so the 'super-rational' solution (if they were playing against a mirror) then they would both choose 'one-half'. This is also the 'cooperate' solution. What I remember about the Prisoner's Dilemma with the classic payouts was that the (paradoxical) Nash equilibrium was that they both defect, as they both then cannot be exploited. So it must be that 17/17 is the Nash equilibrium...but no because they can still be exploited, so...

 

There is no Nash equilibrium.

 

 

(I think...I dunno, I'm bloody tired)

 

Your definition of a Nash equilibrium is a little off, but if you had more faith (and also thought like a corporation), you would have had the right answer with both choosing 17.

It's not that the players can no longer be exploited in a Nash equilibrium, it's that they can obtain no greater benefit from changing their strategies assuming the other players strategy remains the same (and they have knowledge of the strategy).

In this example, if both firms cooperate and produce 1/2 monopoly output, their payoff would be 20. However, they have an incentive to cheat - if each firm thinks the other firm will cooperate (ie produce 1/2), then they can gain greater payoff by producing 2/3 monopoly output.

But if we assume that each firm believes cooperation is not possible because there is no way of enforcing the agreement (output restricting agreements tend to be illegal) then they're in a non-cooperative game - and the clear solution is they gain maximum profit by producing 2/3 monopoly output regardless of what the other firm does.

So what's the implication?

If a Nash Equilibrium is established (by whatever means) there is no incentive for any firm to change its own behaviour.

 

 

 

 

I've been mulling over your post since I woke up. I was about to post "oops, you're right" but then I got to thinking...

 

1) Firstly, technically you may be right about the strict definition of a Nash equilibrium, but poker players think about Nash equilibriums in terms of "not being exploited" because poker is a zero-sum game, and in zero-sum games your definition and my definition have identical consequences.

 

2) Secondly, in the classic Prisoner's Dilemma, the Nash equilibrium is defect/defect because neither player can benefit from changing their behavior. However, in the Firm A/Firm B game, once they are at '17/17,' either firm can benefit from choosing '2/3 monopoly.'

 

Thus there is no Nash equilibrium. They'd just go around in circles.

 

 

Errr limpy - when they're at 17/17 they are already producing 2/3 monopoly output.

 

As to your first point, sorry but you can't just change the definition of something and expect it to have the same meaning. You go look in any micro textbook or journal article and they will define a Nash Equilibrium along the lines I have.

 

 

yeah sorry i meant either can benefit from producing '1/2 monopoly'

thus no Nash equilibrium

 

 

You need to look at that again - if firm A produces at 1/2, then firm B produces at 2/3, is Firm A better off or worse off?

[LimpyLoo]

 

 

 

 

 

 

let's see if i can remember:

 

 

 

Firm B's output will be on the left and firm A's output will be on the right in each quadrant (since I can't do tables in the board there will be no lines, so hopefully this is clear)

 

FIRM A's OUTPUT

One-half Two-Thirds

Monopoly Monopoly

Profit Profit

 

F O One-half

I U Monopoly 20|20 15|22

R T Profit

M P

U

B' T Two-thirds

s Monopoly 22|15 17|17

Profit

 

 

Where's the Nash Equilibrium? Explain your answer, and what are the implications of a Nash equilibrium?

So, a Nash equilibrium occurs when players can no longer exploit each other. The behavior of both players will 'settle' into a Nash equilibrium.

 

Here, there is a question as to whether the two firms can comminucate beforehand, and whether there are meta-game reasons not to cooperate. But if the firms are especially unfriendly they"ll just go in circles trying to exploit each other. And since there is no way to avoid being exploited...

 

Bah I just woke up to piss and now I'm trying to solve game theory puzzles. Alright lemme think here...

 

Okay, so the 'super-rational' solution (if they were playing against a mirror) then they would both choose 'one-half'. This is also the 'cooperate' solution. What I remember about the Prisoner's Dilemma with the classic payouts was that the (paradoxical) Nash equilibrium was that they both defect, as they both then cannot be exploited. So it must be that 17/17 is the Nash equilibrium...but no because they can still be exploited, so...

 

There is no Nash equilibrium.

 

 

(I think...I dunno, I'm bloody tired)

 

Your definition of a Nash equilibrium is a little off, but if you had more faith (and also thought like a corporation), you would have had the right answer with both choosing 17.

It's not that the players can no longer be exploited in a Nash equilibrium, it's that they can obtain no greater benefit from changing their strategies assuming the other players strategy remains the same (and they have knowledge of the strategy).

In this example, if both firms cooperate and produce 1/2 monopoly output, their payoff would be 20. However, they have an incentive to cheat - if each firm thinks the other firm will cooperate (ie produce 1/2), then they can gain greater payoff by producing 2/3 monopoly output.

But if we assume that each firm believes cooperation is not possible because there is no way of enforcing the agreement (output restricting agreements tend to be illegal) then they're in a non-cooperative game - and the clear solution is they gain maximum profit by producing 2/3 monopoly output regardless of what the other firm does.

So what's the implication?

If a Nash Equilibrium is established (by whatever means) there is no incentive for any firm to change its own behaviour.

 

 

 

 

I've been mulling over your post since I woke up. I was about to post "oops, you're right" but then I got to thinking...

 

1) Firstly, technically you may be right about the strict definition of a Nash equilibrium, but poker players think about Nash equilibriums in terms of "not being exploited" because poker is a zero-sum game, and in zero-sum games your definition and my definition have identical consequences.

 

2) Secondly, in the classic Prisoner's Dilemma, the Nash equilibrium is defect/defect because neither player can benefit from changing their behavior. However, in the Firm A/Firm B game, once they are at '17/17,' either firm can benefit from choosing '2/3 monopoly.'

 

Thus there is no Nash equilibrium. They'd just go around in circles.

 

 

Errr limpy - when they're at 17/17 they are already producing 2/3 monopoly output.

 

As to your first point, sorry but you can't just change the definition of something and expect it to have the same meaning. You go look in any micro textbook or journal article and they will define a Nash Equilibrium along the lines I have.

 

 

yeah sorry i meant either can benefit from producing '1/2 monopoly'

thus no Nash equilibrium

 

 

You need to look at that again - if firm A produces at 1/2, then firm B produces at 2/3, is Firm A better off or worse off?

 

 

Okay, so you're saying the Nash equilibrium is 'two-thirds'/'two-thirds' (aka 17/17).

 

If that were true, then neither firm could benefit from straying from the Nash equilibrium. But when they're at (17/17), either firm can switch to 'one-half' and improve their payout. Therefor it's not a Nash equilibrium.

[LimpyLoo]

lemme know if/when we should consult google

[mcbpete]

 

mcbpete? more like..................

 

......

 

 

 

......

 

.....

 

......

 

.....

 

MC BEE PETE

 

Funnily enough that's how the Scottish folks pronounce it (at 39m22s) -

Linky link

[DerWaschbar]

put 2 cats in a pillow case you got a game in theory

[chenGOD]

They can only improve their payout if the other firm also moves to 1/2 monopoly output.

 

Look I'll run it through again for you. Let's assume Firm A and Firm B start at the position of both producing 2/3 monopoly output. In this case their payout is 17. Now, if they both switched to 1/2 monopoly output, yes they would improve their payout. However, if both firms are at 1/2 monopoly output, they have an incentive to cheat.

If Firm A moves to 2/3 output while Firm B remains at 1/2, Firm A's payoff becomes 22 while Firm B's payoff becomes 15. So Firm B has no incentive to move to 1/2 monopoly production.

[LimpyLoo]

They can only improve their payout if the other firm also moves to 1/2 monopoly output.

 

Look I'll run it through again for you. Let's assume Firm A and Firm B start at the position of both producing 2/3 monopoly output. In this case their payout is 17. Now, if they both switched to 1/2 monopoly output, yes they would improve their payout. However, if both firms are at 1/2 monopoly output, they have an incentive to cheat.

If Firm A moves to 2/3 output while Firm B remains at 1/2, Firm A's payoff becomes 22 while Firm B's payoff becomes 15. So Firm B has no incentive to move to 1/2 monopoly production.

 

The whole idea of a Nash equilibrium is that, as with'defect/defect' in PD, neither player can (unilaterally) improve their payout by switching.

 

This isn't the case with '17/17.' If I'm Firm A and you're Firm B, then I will switch to '1/2' and improve my payout. This can't happen with 'defect/defect' in PD. Neither player can (unilaterally) improve by switching.

 

Therefor '17/17' is not a Nash equilibrium, and the game is more akin to rock-paper-scissors than PD.

[YangYing]

 

 

They can only improve their payout if the other firm also moves to 1/2 monopoly output.

 

Look I'll run it through again for you. Let's assume Firm A and Firm B start at the position of both producing 2/3 monopoly output. In this case their payout is 17. Now, if they both switched to 1/2 monopoly output, yes they would improve their payout. However, if both firms are at 1/2 monopoly output, they have an incentive to cheat.

If Firm A moves to 2/3 output while Firm B remains at 1/2, Firm A's payoff becomes 22 while Firm B's payoff becomes 15. So Firm B has no incentive to move to 1/2 monopoly production.

 

The whole idea of a Nash equilibrium is that, as with'defect/defect' in PD, neither player can (unilaterally) improve their payout by switching.

 

This isn't the case with '17/17.' If I'm Firm A and you're Firm B, then I will switch to '1/2' and improve my payout. This can't happen with 'defect/defect' in PD. Neither player can (unilaterally) improve by switching.

 

Therefor '17/17' is not a Nash equilibrium, and the game is more akin to rock-paper-scissors than PD.

 

i have diarrhea

 

edit: this is the most bizarre thread i have read since that time the mods decided to fuck around with the backgrounds and fonts of the forum

[chenGOD]

If Firm A produces at 1/2 monopoly output and Firm B produces at 2/3 monopoly output what do you think each firms' respective payouts will be?

[peace 7]

a mathematical discipline articulated by John Nash and other early pioneers in the fields of discrete math and computer science. used to describe the interactions of complex elements in various 'states of play', like a 'game'. often cited by pretentious cunts in discussions to which it is not particularly relevant or enlightening, because of its appeal in popular science.

 

Yah, I imagine this is actually sort of true.

 

Here's the top part of a flyer I designed a couple years ago for a Tokyo University thing:

 

 

So after designing that, I went pirate mode and downloaded a few books on game theory-- the most interesting part for me was the potential for a totally different method on how one could approach life. By applying game theory and related maths to everyday events and even long term goals, I realized that life could be executed very much like an RPG-- as in, living one's life like playing Dungeon's and Dragons.

 

For those of you who are reverse-hippie, anti-vibe, and prefer cold and calculated orgasms, I recommend life with game theory application. You might do quite well, quite easily.

[YangYing]

 

a mathematical discipline articulated by John Nash and other early pioneers in the fields of discrete math and computer science. used to describe the interactions of complex elements in various 'states of play', like a 'game'. often cited by pretentious cunts in discussions to which it is not particularly relevant or enlightening, because of its appeal in popular science.

 

Yah, I imagine this is actually sort of true.

 

Here's the top part of a flyer I designed a couple years ago for a Tokyo University thing:

 

 

So after designing that, I went pirate mode and downloaded a few books on game theory-- the most interesting part for me was the potential for a totally different method on how one could approach life. By applying game theory and related maths to everyday events and even long term goals, I realized that life could be executed very much like an RPG-- as in, living one's life like playing Dungeon's and Dragons.

 

For those of you who are reverse-hippie, anti-vibe, and prefer cold and calculated orgasms, I recommend life with game theory application. You might do quite well, quite easily.

 

oh, how would game theory apply to, for example, say.. your next post on this thread?

 

edit: and how would the post look if we instead used reverse-hippie and/or anti-vibe principals?

 

edit2: I ask because I want to do well in life and haven't been able to decide how to approach life or if it should be approached at all or if just nothing is real and shit like that, u know, like posting on idm forums.

[LimpyLoo]

If Firm A produces at 1/2 monopoly output and Firm B produces at 2/3 monopoly output what do you think each firms' respective payouts will be?

 

FIRM A's OUTPUT

One-half Two-Thirds

Monopoly Monopoly

Profit Profit

 

F O One-half

I U Monopoly 20|20 15|22

R T Profit

M P

U

B' T Two-thirds

s Monopoly 22|15 17|17

Profit

 

 

So the right hand corner, A gets 15 and B gets 22?

 

bah okay i should've looked closer

you're right

 

 

edit: hold on a second...

[LimpyLoo]

so if I'm Firm A, and you're Firm B

 

and we're at 'two-thirds'/'two-thirds' (aka '17/17')

 

if I (Firm A) switch to 'one-half"

will i not get '22', and you '15'?

 

if that is indeed true, then '17/17' is not a Nash equilibrium

but i might be reading the matrix wrong

[oh2]

(1/2,1/2)-> no eq since 2/3 would benefit firm A

(1/2,2/3)-> no eq since 2/3 would benefit firm B

(2/3,1/2)-> no eq since 2/3 would benefit firm B

(2/3,2/3) -> if A chooses 2/3 first, we see B is better off with 2/3, if B chooses 2/3 first

we see A is better off with 2/3, thus this is an eq

[LimpyLoo]

 

(1/2,1/2)-> no eq since 2/3 would benefit firm A

(1/2,2/3)-> no eq since 2/3 would benefit firm B

(2/3,1/2)-> no eq since 2/3 would benefit firm B

(2/3,2/3) -> if A chooses 2/3 first, we see B is better off with 2/3, if B chooses 2/3 first

we see A is better off with 2/3, thus this is an eq

 

 

but in order for it to be a Nash Equilibrium, (2/3,2/3) must remain 'stable' (ergo "equilibrium")

 

but once at (2/3,2/3) either player can benefit by unilaterally switching to '1/2'

and so around and around they go

[chenGOD]

so if I'm Firm A, and you're Firm B

 

and we're at 'two-thirds'/'two-thirds' (aka '17/17')

 

if I (Firm A) switch to 'one-half"

will i not get '22', and you '15'?

 

if that is indeed true, then '17/17' is not a Nash equilibrium

but i might be reading the matrix wrong

You're reading the matrix wrong.

[Guest kymppinetti]

https://en.wikipedia.org/wiki/Zero_Escape:_Virtue%27s_Last_Reward

[LimpyLoo]

 

so if I'm Firm A, and you're Firm B

 

and we're at 'two-thirds'/'two-thirds' (aka '17/17')

 

if I (Firm A) switch to 'one-half"

will i not get '22', and you '15'?

 

if that is indeed true, then '17/17' is not a Nash equilibrium

but i might be reading the matrix wrong

You're reading the matrix wrong.

 

 

oh okay that explains it

you're right then

[YangYing]

what would the rules for the game theory music genre be?

 

edit: what does game theory taste like?

 

edit2: what does it smell like?

 

edit3: how does it feel to get it up your ass?

 

edit4: this is such an exciting topic

 

edit5: why are 13 people reading a thread with the topic name "game theory" on a forum devoted to bleep bloop music?

[LimpyLoo]

so wait...you set it up so it's (B, A)?

 

If Firm A produces at 1/2 monopoly output and Firm B produces at 2/3 monopoly output what do you think each firms' respective payouts will be?

 

FIRM A's OUTPUT
One-half Two-Thirds
Monopoly Monopoly
Profit Profit

F O One-half
I U Monopoly 20|20 15|22
R T Profit
M P
U
B' T Two-thirds
s Monopoly 22|15 17|17
Profit

 

so you're saying the payouts are (B,A)?

 

are you sure YOU'RE not misreading the matrix?

[oh2]

consider (2/3,2/3)

if firm B changes from 2/3->1/2 they go from 17-15

if firm A changes from 2/3->1/2 they go from 17-15

thus in each outcome, a change of decision for the player results in a worse outcome,

therefore this is a nash eq by definition

[LimpyLoo]

if it's (A,B) then i'm right and there is no Nash equilibrium

 

if it's (B,A) then... why the hell is it (B,A)? lol

 

consider (2/3,2/3)

if firm B changes from 2/3->1/2 they go from 17-15

if firm A changes from 2/3->1/2 they go from 17-15

thus in each outcome, a change of decision for the player results in a worse outcome,

therefore this is a nash eq by definition

 

 

let's wait to hear from Chen about the (A,B) or (B,A) thing

 

once there's clarification this'll be easy as cheese to sort out

[chenGOD]

so wait...you set it up so it's (B, A)?

 

If Firm A produces at 1/2 monopoly output and Firm B produces at 2/3 monopoly output what do you think each firms' respective payouts will be?

 

FIRM A's OUTPUT

One-half Two-Thirds

Monopoly Monopoly

Profit Profit

 

F O One-half

I U Monopoly 20|20 15|22

R T Profit

M P

U

B' T Two-thirds

s Monopoly 22|15 17|17

Profit

 

 

 

so you're saying the payouts are (B,A)?

 

are you sure YOU'RE not misreading the matrix?

 

100% sure. If both firms are producing at 1/2 then the payout is 20/20. If both firms are producing at 2/3, then the payout is 17/17.

If Firm A produces at 1/2 monopoly output and Firm B produces at 2/3 monopoly output, (ie bottom left quadrant) Then Firm A's payout is 15 while Firm B's payout is 22.

 

edit: yes the payout is (B,A)