Talk:Hotelling's law

Why a third?

"It would be more socially beneficial if the shops separated themselves and moved to one third of the way along the street at different ends". Why a third? Would a quarter be even better? --Henrygb 18:38, 8 Mar 2005 (UTC)

because that is overall closest to as many places as possible, well that is the reasoning, you would have to ask a mathematician for the exact optimal distance. Bluemoose 19:47, 8 Mar 2005 (UTC)

I am a mathematician and I think a quarter would be better. Anyone give me a good reason why not?--Henrygb 23:58, 8 Mar 2005 (UTC)

It seems to me that 1/4 would be better as well. That should minimize the distance any person would need to walk to reach a store. Assuming someone is coming from either end, they only need to walk 1/4 of the length of the street to reach a shop, and so would someone in the middle of the street. If they were located 1/3 apart, people on the ends would have to walk farther, even though people in the middle would have a shorter distance. This case could possibly be a better solution if the density of people is significantly greater in the center of the street, but assuming uniform probabilities of starting location, 1/4 would be better. KristinLee 01:19, 9 May 2006 (UTC)

Multiple shops

As I remember it from my economics degree, Hotelling's law only applies to two shops: there is no equilibrium for n of shops>2. Can someone who knows more about this confirm and add? Chris Martin 23:36, 16 May 2006 (UTC)

Well for 3 I tried and couldnt find any stable formations, but with four there seems to be at least one equilibrium point (for a 20 long row of houses, place the four shops at the 5th, 6th, 15th and 16th spots and they all have 4 customers each, and no position can be moved to that gets more than 4 customers). As a guess if the number of customers is divisible by the number of shops, and their is an even number of shops you can have an equilibrium (whether in practise the equilibrium can be achieved by individual maximisation efforts by each shop is open to question without playing with it more, but that depends a lot of your assumptions about when and how each shop moves). -- 86.128.253.74 15:06, 11 October 2006 (UTC)

While there is no stable equilibrium for three shops, it seems to me that the shops would still tend towards the center. Assume 1. that shops are myopic and only predict the effect of a single turn in the future; 2. shops don't move simultaneously. First, regardless of starting positions, within one turn, two shops would be right next to each other (as predicted by the n=2 hotelling model.) Next, the third shop would join the other two. Slowly the shops would move toward the center. If shops cannot sit on top of each other, one shop would be stuck in the middle (eg a,|b|,c), 'b' would jump to one unit outside one of the other shops (eg a,| |,c,b). Now, 'c' would move outside 'a' or 'a' would move into the center (eg c,a,| |, ,b or |a|,c,b ). While the specific variations are numerous, there is a clear tendency to capture the middle and then get surrounded. Adding transaction costs would likely radically change the outcome.

PaperTyler (talk) 05:07, 15 December 2008 (UTC)

Hotelling effect?

Somebody started an article called the Hotelling Effect. They created said article, then disambiguated a link 3 months later, now it's been a year and a half with no other edits. After linking Harold Hotelling, I discovered the Law article. If no one objects, I'll merge in the substance of the other article into an extra illustrative application. Xaxafrad 14:35, 27 July 2006 (UTC)

Okay, I WAS going to add this in:

<block>Alternately, assume two snack vendors are peddling on a beach of length X (running from 0 to X), one is at .25X and one is at .75X -- they each have access to .5X and will get half the consumers on the beach who want snacks (assuming people walk to the nearest carts, prices, selection and service are the same, etc.). When the first vendor moves to .33X he still gets everyone from 0 - .33X coming to him, but now gets half the people from .33X - .75X, stealing business from the second guy, who promptly moves to .66X to make up for it. Eventually they end up at .49X and .51X (or both at .50X if you want), glaring at each other, each still getting 50% of the business, any intermediate gains lost. The people at the far ends of the beach suffer as a result. However, this leaves open the possibility that a third and fourth entrepreneur may capitalize on the convience-seeking of the beach-goers at both ends. If the original vendors had taken an economics class, they might have foreseen this outcome and stayed where they were.

John Hopkins Magazines, April 1997 </block>

but it's a might not be encyclopedic quality. Second opinions? Xaxafrad 15:01, 27 July 2006 (UTC)

I don't think this extra example adds anything considering how much it would need to be cleaned up, if people want an extra example for clarity it would be as useful to create one from scratch I think. -- 86.128.253.74 14:45, 11 October 2006 (UTC)

"perfect location for two ice cream vendors on the beach" theory

There is an economic theory abut where two ice cream vendors who sell an identical product end up on a beach (right in the middle). There's a Wikipedia article about it and I wanted to link to it as it is the same idea just in economics - but I can't find it. But it exists because i know I read it. If you can think of it, please add it, thanks a lot.--Soylentyellow 22:45, 23 May 2007 (UTC)

Isnt this example of two ice cream vendors interpret better as Nash equilibrium? — Preceding unsigned comment added by 211.25.178.4 (talk) 06:29, 4 March 2016 (UTC)

On Hotelling's "Stability in Competition"

There is a note in Econometrica:

Econometrica, Vol. 47, No. 5 (September, 1979) ON HOTELLING'S "STABILITY IN COMPETITION" BY C. D'ASPREMONT, J. JASKOLD GABSZEWICZ, AND J.-F. THISSE

They state that "The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling's 1929 paper "Stability in Competition," is invalid. Firstly, we assert that, contrary to the statement formulated by Hotelling in his model, nothing can be said about the tendency of both sellers to agglomerate at the center of the market. The reason is that no equilibrium price solution will exist when both sellers are not far enough from each other. Secondly, we consider a slightly modified version of Hotelling's example, for which there exists a price equilibrium solution everywhere. We show however that, for this version, there is a tendency for both sellers to maximize their differentiation. This example thus constitutes a counterexample to Hotelling's conclusions." —Preceding unsigned comment added by Mogens1 (talk • contribs) 19:18, 24 June 2008 (UTC)

high importance

I changed the importance of this article from Low to High. For a discussion, see Wikipedia talk:WikiProject Economics/Assessment. --PaperTyler (talk) 05:54, 15 December 2008 (UTC)

I've switched it to Mid, possibly will want to switch to Low later--trying to get better proportions in the importance categories. CRETOG8(t/c) 07:10, 23 December 2008 (UTC)

Dr. Platen's comment on this article

Dr. Platen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

This is well written and understandable to a wide readership.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Platen has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.

ExpertIdeasBot (talk) 14:55, 24 June 2016 (UTC)

Proposed deletion

Before I list this at WP:AfD, does anyone want to add sources that establish this article meeting the requirements of WP:GNG? --Guy Macon (talk) 12:45, 17 May 2019 (UTC)

While it doesn't have a lot of sources, the article is not unsourced. Google searches seem to suggest that the concept and the name are generally understood in economics, and occasionally referenced in less formal contexts. What aspects of GNG are you concerned about?

This will certainly end up as a 'no consensus' at worst, and likely a 'keep' at AfD. So unless you're hoping to use AfD (or the thread of AfD) as a way to force a cleanup of the article, you're probably barking up the wrong tree. (And honestly, there are other articles that much more desperately need to have attention forced up on them, if you're trying to use AfD that way.) TenOfAllTrades(talk) 13:01, 17 May 2019 (UTC)