<p>Here is a link to <a href="http://www.stern.nyu.edu/networks/phdcourse/Schmalensee%20_Entry_deterrence.pdf" rel="nofollow noreferrer">Schmalansee's classic paper</a>.  Use SSRI to look forward in time from this paper.  Useful search terms in Econlit or Google Scholar would be "crowding the product space" or "product space congestion."</p>

CC BY-SA 3.0
2016-12-13T14:21:20.840Z
2016-12-13T14:21:20.840Z
Bill
<p>In the strict classical Hotelling model, it is impossible to have an equilibrium with 3 agents over the segment (deviation is always profitable). Some modification have been done to keep the transportation costs+inelastic demand with $n$ firms (with multiple segments and a common point, like a flake).</p>

<p>By the way, d'Aspremont et al. modified the cost function to reach "their" equilibrium.</p>

CC BY-SA 3.0
2016-12-13T14:07:11.100Z
It is not true that equilibrium is always symmetric. There is a characterisation of the classic equilibria (linear cost, as in Hotelling's paper) for $n$ players in [Eaton (1975)](https://www.jstor.org/stable/2296817) and for $n > 5$ asymmetric equilibria exist.
Giskard
CC BY-SA 3.0
2016-12-13T16:52:55.237Z
Accurate! I'm glad my answer raised a bit of attention to this unanswered question, nevertheless I would be happy to delete it (and in this case your link would disappear). Do you think you could write an answer?
Yann
CC BY-SA 3.0
2016-12-13T21:18:39.787Z
No need to delete it. Perhaps edit out the always symmetric part. I don't know what the exact question is. I think your comment under the question is important. It is a shame it was not answered.
Giskard
CC BY-SA 3.0
2016-12-13T13:36:21.977Z
2016-12-13T22:15:54.110Z
2016-12-13T22:15:54.110Z
Yann
<p>I am having difficulty modelling the effect of horizontal product differentiation between multiproduct firms. I've been looking at models specifically by Hotelling and d'Aspremont. Hotelling concluded that in duopolistic competition, an equilibrium was found through firms differentiating minimally, (i.e. designing products of similar attributes) whilst d’Aspremont shows the opposite with the equilibria resting at maximal product differentiation.</p>

<p>However, both of these principles do not take into account multiproduct firms, where firms could produce different varieties of the same product (take shoes for example) where some are highly differentiated and others may be similar to a competitor. Is there a model that explains this situation?</p>

CC BY-SA 3.0
2016-12-05T22:21:33.287Z
Could you specify the kind of multi-product firms you have in mind? N>2 products over a single line or k lines of products where only two firms compete, with scale economies?
Yann
<reference-request><product-differentiation>
Multiproduct firms and horizontal product differentiation
Ryan
# Multiproduct firms and horizontal product differentiation

(Asked by: username_0 on 2016-12-05)

I am having difficulty modelling the effect of horizontal product differentiation between multiproduct firms. I've been looking at models specifically by Hotelling and d'Aspremont. Hotelling concluded that in duopolistic competition, an equilibrium was found through firms differentiating minimally, (i.e. designing products of similar attributes) whilst d’Aspremont shows the opposite with the equilibria resting at maximal product differentiation.

However, both of these principles do not take into account multiproduct firms, where firms could produce different varieties of the same product (take shoes for example) where some are highly differentiated and others may be similar to a competitor. Is there a model that explains this situation?

**Tags:** reference-request, product-differentiation

> **Comments:**
> **username_1**: Could you specify the kind of multi-product firms you have in mind? N>2 products over a single line or k lines of products where only two firms compete, with scale economies?  

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## 2 answers

### Answer by username_2 on 2016-12-13. Score: 2

Here is a link to [Schmalansee's classic paper](http://www.stern.nyu.edu/networks/phdcourse/Schmalensee%20_Entry_deterrence.pdf). Use SSRI to look forward in time from this paper. Useful search terms in Econlit or Google Scholar would be "crowding the product space" or "product space congestion."


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### Answer by username_1 on 2016-12-13. Score: 1

In the strict classical Hotelling model, it is impossible to have an equilibrium with 3 agents over the segment (deviation is always profitable). Some modification have been done to keep the transportation costs+inelastic demand with $n$ firms (with multiple segments and a common point, like a flake).

By the way, d'Aspremont et al. modified the cost function to reach "their" equilibrium.

> **Comments:**
> **username_3**: It is not true that equilibrium is always symmetric. There is a characterisation of the classic equilibria (linear cost, as in Hotelling's paper) for $n$ players in [Eaton (1975)](https://www.jstor.org/stable/2296817) and for $n > 5$ asymmetric equilibria exist.  
> **username_1**: Accurate! I'm glad my answer raised a bit of attention to this unanswered question, nevertheless I would be happy to delete it (and in this case your link would disappear). Do you think you could write an answer?  
> **username_3**: No need to delete it. Perhaps edit out the always symmetric part. I don't know what the exact question is. I think your comment under the question is important. It is a shame it was not answered.  

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