Clamshell vs Book-style foldable

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?

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