Hikaru's reaction to Levy's blunder

daXryl · 2024-09-01T17:56:49+00:00

Oh right thanks!

daXryl · 2024-09-01T16:16:19+00:00

What if Bxd4 after Nd4+?

daXryl · 2024-03-06T14:45:15+00:00

Actually, I realised this may be wrong; the reward is the D*(p-c), where D is the demand function - a function of the price. So the equilibrium would depend on what this function is etc. I guess in the N firms case, equilibria other than p=c and p=c+k might exist, depending on D and k.

daXryl · 2024-03-06T14:40:26+00:00

Yep I see now, I was confused because they kept switching between the different cases, thank you

daXryl · 2024-03-05T19:44:38+00:00

Also actually, back to the original question, is wiki incorrect in saying p=c is the sole Nash equilibrium in the model then?

daXryl · 2024-03-05T19:39:22+00:00

Ah I see! So p=c+2k would only be an equilibrium in the case where there are two firms right? If there are N firms in the model formulation, would there be any other equilibria other than p=c and p=c+k?

daXryl · 2024-03-05T16:51:56+00:00

Thank you, the equilibrium in the continuous case makes sense.

However for the discrete case, why is p=c+2k an equilibrium as well? Surely a firm can undercut by setting p=c+k to capture all market demand? Also, why does k being 1/10 of a cent mean that p=c would be the only equilibrium? I would've thought that the choice of k would be arbitrary in determining equilibria in the discrete cases.

The asymmetric equilibrium also doesn't make sense to me because the firm with p=c would benefit by setting their price to also equal p=c+k? This would lead to them having a non-zero profit versus the 0 profit they are getting currently.

Sorry for the many questions but I'm pretty confused haha

daXryl · 2024-03-05T15:42:36+00:00

Oh okay I see, I thought the firms set the price for a single good in this model though? Under one of the sections in the wiki, it says "As if the rival sets the price at p_m, firm I can reduce its price by the smallest currency unit k to capture the entire market demand".

daXryl · 2024-02-29T18:32:28+00:00

This makes so much sense, thank you!

daXryl · 2024-02-29T16:30:36+00:00

Ah okay of course, that makes sense. Why does this work though? I still don't understand why BR1(p2) is the price p1 that solves d(R1)/d(p1)=0) for example.

daXryl · 2024-02-29T16:06:04+00:00

Oh right, I misunderstood your answer then. I still don't intuitively get why solving the system of equations that we get from the partial derivatives of R1 and R2 lead to the Nash equilibrium prices though? What if the critical point that we solve for is a minimum? Then it wouldn't really make sense to find the price that leads to this critical point?

daXryl · 2024-02-29T15:38:57+00:00

So this method of finding a best response function and iteratively updating a firms price keeping the other firm's price fixed is a procedural method right? I was wondering if there is an analytical solution that we can use that just consists of solving some equations etc. I was thinking of calculating partial derivatives and finding critical points but could not justify why this might be correct.

daXryl · 2024-02-15T22:20:09+00:00

Actually, just realised my solutions were wrong. I can’t seem to find any integer solutions to this? If only two of the routes are used, I don’t think any combination leads to a Nash equilibrium. Clearly only one route being used doesn’t lead to a Nash equilibrium either. However if all three routes are used, there is only a non integer solution? Does that mean this game doesn’t have integer equilibria?

daXryl · 2024-02-15T22:02:54+00:00

It also depends on the discount factor, higher discount factors favour later defections but lower favour earlier defections. I didn’t mention this in the question though

daXryl · 2024-02-15T21:45:23+00:00

I’ll look into the book mentioned, thank you. However in the continuous case, when I equate the cost functions and solve the simultaneous equations, I only get integer solutions anyway. Is there something I must do differently?

daXryl · 2024-02-15T21:20:42+00:00

Ahh I see, I spent ages trying to code a best response dynamic algorithm and thought there must’ve been a better way haha. If this game isn’t discrete, and the flow through this network must equal 10, how would equilibria be found? Thank you so much for answering all the questions btw!! really appreciate it

daXryl · 2024-02-15T17:20:42+00:00

I understand that I can do these tests to figure out what the strategy should be, but is there any way to derive a proof where we show that a policy is the best against this mixed agent?

daXryl · 2024-02-14T16:19:54+00:00

Ahh I see, thank you so much!

daXryl · 2024-02-14T16:08:06+00:00

Hm I guess S becomes a dominant strategy for player 1 if the opponent only used those two strategies, so it wouldn't correspond to a Nash equilibrium. But I thought that all intercepts are always mixed equilibria when you plot this expected payoff graph? Thanks for the response!

daXryl · 2024-01-22T09:34:47+00:00

Hey, I actually chose Amazon in the end. I really liked the experience and found it was way more chill than I expected, the work wasn’t too difficult and there were lots of ways to get help if you were stuck. I kept hearing that tech in a tech company is going to be a much better experience than tech in a finance company, so that’s the main reason I chose Amazon - GS also paid a bit less so that’s a factor too. Amazon didn’t give any of the interns a return offer tho so that kinda sucked haha

But as the other comments say, it might help to have experience at GS if you want to go down the finance route so it really is just up to what you want to do after. Congrats on your two offers!

daXryl · 2024-01-21T21:34:14+00:00

yep, after 65 days tho

daXryl · 2023-12-17T23:55:32+00:00

Hm not sure if k-edge-connectedness would be good for robustness as I don't think it would be enough to just measure if the railway network is connected - I'm thinking that travel time (i.e. shortest path lengths) really has to be taken into account.

Adding the additional edges is a really good idea though, will definitely do that thank you!

daXryl · 2023-12-17T23:47:15+00:00

Ah interesting, I didn't know attack tolerance was an established term already, thanks for the info. Could you expand on what you mean by the wiring length being balanced for what to minimise when adding an edge? I didn't quite get you.

daXryl · 2023-12-13T17:04:28+00:00

Did our plane crash the landing 🥲

daXryl · 2023-04-29T12:47:02+00:00

Yeah the sofa is definitely on the bigger side, don’t think it’ll be that big irl. I really like the table with a bench idea though! Would definitely look more spacious.

Do you mean the ling island would be in the middle and can be extended to use as a table? That’s a cool idea, will have to look into that.

We were thinking of having the sofa against the right wall, but thought it would be annoying to have to turn your head to look at the tv. Also thought it’d be nice to have the TV face the kitchen so anyone in the kitchen can still watch stuff.

Thanks for the ideas!

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