<p>This <a href="https://onlinelibrary.wiley.com/doi/10.1002/nav.21486" rel="nofollow noreferrer">operations research</a> paper considers a &quot;Cournot&quot; competition modeled as follows.</p>
<blockquote>
<p>[E]ach [firm] <span class="math-container">$i$</span> incurs a cost <span class="math-container">$w$</span> in obtaining one
unit of the product, sells <span class="math-container">$q_i$</span> units of the product at a unit price
<span class="math-container">$p_i$</span> , and generates a proﬁt <span class="math-container">$π_i (q_1 , q_2)$</span> when the two retailers
sell <span class="math-container">$q_1$</span> and <span class="math-container">$q_2$</span> units of the product, respectively. We have
<span class="math-container">$p_i = z_i − (q_1 + q_2)$</span>
and
<span class="math-container">$π_i (q_1 , q_2) = (p_i − w)q_i = (z_i − (q_1 + q_2) − w)q_i$</span>,
for <span class="math-container">$i = 1, 2$</span>,
where for the same quantity sold, a retailer with a larger <span class="math-container">$z_i$</span>
charges a higher price for the product.</p>
</blockquote>
<p>(Presumably, the prices are normalized so that they have the same unit as quantities.)  Based on what little I have read about Cournot competitions, it seems odd that there are two different prices for the same goods (unless <span class="math-container">$z_1 = z_2$</span>, but interesting things happen only if <span class="math-container">$z_1 \neq z_2$</span> in this article).  Is this model reasonably be called a Cournot competition?</p>
<p>I concede that this model gives the same equilibrium as the Cournot duopoly in which the marginal cost incurred to each firm is <span class="math-container">$w_i$</span> and the common price is <span class="math-container">$p_0 - (q_1 + q_2)$</span>, where <span class="math-container">$p_0$</span>, <span class="math-container">$w_1$</span>, <span class="math-container">$w_2$</span> are chosen so that <span class="math-container">$p_0 - w_i = z_i - w$</span> and that the relevant quantities are nonnegative.  Still I find that presentation in the article weird.</p>
<p>(I guess it's possible, albeit unfortunate, that this is what's called a Cournot competition in operations research even if it's not in economics.)</p>

CC BY-SA 4.0
2024-08-21T02:12:56.873Z
What is $z_i$? Is it $i$'s capacity?
Herr K.
CC BY-SA 4.0
2024-08-21T02:56:33.177Z
@HerrK. It's a mystery parameter not explained in the paper.  Cho and Tang, who cite the paper, say that it "represents retailer i’s “market power” that captures her comparative advantage over her competitors due to certain factors including location, customer loyalty, and brand reputation" and put a reference to a seemingly unrelated paper.
Pteromys
CC BY-SA 4.0
2024-08-21T03:36:20.847Z
I only took a quick peak at the paper. At the beginning of Section 2, the author does say: "We consider Cournot competition, that is, the two retailers ***compete on the quantity*** of the product they sell." This is consistent with the common understanding of Cournot competition as one on *quantities*. It is conceivable that (a variant of) such competition occurs between [rivals with differentiated characteristics](https://www.google.com/search?q=cournot+with+differentiated+products) (here the differentiation is measured by $z_i$), which could lead to differentiated prices in equilibrium.
Herr K.
CC BY-SA 4.0
2024-08-21T09:52:08.790Z
@HerrK My reservation is that the goods from each firm (or a retailer in their example) are sourced from the same person and thus complete substitutes, in which case I don't see there being two different prices.
Pteromys
CC BY-SA 4.0
2024-08-21T15:00:29.963Z
I don't want to defend someone else's work (especially when I haven't read it in detail). But here's how I'd make sense of the setup. The subscript $i$ in the parameter $z_i$ suggests the two retailers effectively face different demands. In other words, from the customer's perspective, the two firms' products are not perfect substitutes. For example, Esso vs some no-name gas station both sell the same product, gasoline, but the former may attract more customers (higher $z_i$) thanks to the brand recognition. Nevertheless, I do agree that the paper is somewhat confusing about the model's setup.
Herr K.
CC BY-SA 4.0
2024-08-21T15:07:39.087Z
The bottom line is, as long as the competition is about simultaneous decisions on quantity, then it can be called a Cournot competition, or at least a variant thereof. Whether the competition leads to the same result as the classic Cournot model that appears in most textbooks is a different matter.
Herr K.
<microeconomics><definition><oligopoly><cournot>
"Cournot competition" with different prices for different firms
Pteromys
# "Cournot competition" with different prices for different firms

(Asked by: username_0 on 2024-08-21)

This [operations research](https://onlinelibrary.wiley.com/doi/10.1002/nav.21486) paper considers a "Cournot" competition modeled as follows.

> [E]ach [firm] $i$ incurs a cost $w$ in obtaining one
> unit of the product, sells $q\_i$ units of the product at a unit price
> $p\_i$ , and generates a proﬁt $π\_i (q\_1 , q\_2)$ when the two retailers
> sell $q\_1$ and $q\_2$ units of the product, respectively. We have
> $p\_i = z\_i − (q\_1 + q\_2)$
> and
> $π\_i (q\_1 , q\_2) = (p\_i − w)q\_i = (z\_i − (q\_1 + q\_2) − w)q\_i$,
> for $i = 1, 2$,
> where for the same quantity sold, a retailer with a larger $z\_i$
> charges a higher price for the product.

(Presumably, the prices are normalized so that they have the same unit as quantities.) Based on what little I have read about Cournot competitions, it seems odd that there are two different prices for the same goods (unless $z\_1 = z\_2$, but interesting things happen only if $z\_1 \neq z\_2$ in this article). Is this model reasonably be called a Cournot competition?

I concede that this model gives the same equilibrium as the Cournot duopoly in which the marginal cost incurred to each firm is $w\_i$ and the common price is $p\_0 - (q\_1 + q\_2)$, where $p\_0$, $w\_1$, $w\_2$ are chosen so that $p\_0 - w\_i = z\_i - w$ and that the relevant quantities are nonnegative. Still I find that presentation in the article weird.

(I guess it's possible, albeit unfortunate, that this is what's called a Cournot competition in operations research even if it's not in economics.)

**Tags:** microeconomics, definition, oligopoly, cournot

> **Comments:**
> **username_1**: What is $z_i$? Is it $i$'s capacity?  
> **username_0**: @HerrK. It's a mystery parameter not explained in the paper.  Cho and Tang, who cite the paper, say that it "represents retailer i’s “market power” that captures her comparative advantage over her competitors due to certain factors including location, customer loyalty, and brand reputation" and put a reference to a seemingly unrelated paper.  
> **username_1**: I only took a quick peak at the paper. At the beginning of Section 2, the author does say: "We consider Cournot competition, that is, the two retailers ***compete on the quantity*** of the product they sell." This is consistent with the common understanding of Cournot competition as one on *quantities*. It is conceivable that (a variant of) such competition occurs between [rivals with differentiated characteristics](https://www.google.com/search?q=cournot+with+differentiated+products) (here the differentiation is measured by $z_i$), which could lead to differentiated prices in equilibrium.  
> **username_0**: @HerrK My reservation is that the goods from each firm (or a retailer in their example) are sourced from the same person and thus complete substitutes, in which case I don't see there being two different prices.  
> **username_1**: I don't want to defend someone else's work (especially when I haven't read it in detail). But here's how I'd make sense of the setup. The subscript $i$ in the parameter $z_i$ suggests the two retailers effectively face different demands. In other words, from the customer's perspective, the two firms' products are not perfect substitutes. For example, Esso vs some no-name gas station both sell the same product, gasoline, but the former may attract more customers (higher $z_i$) thanks to the brand recognition. Nevertheless, I do agree that the paper is somewhat confusing about the model's setup.  
> **username_1**: The bottom line is, as long as the competition is about simultaneous decisions on quantity, then it can be called a Cournot competition, or at least a variant thereof. Whether the competition leads to the same result as the classic Cournot model that appears in most textbooks is a different matter.  

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## 0 answers

