<p>Even if firms have identical technologies and identical reaction functions, the Cournot equilibrium can be asymmetric, as shown there:</p>
<p>Amir, Rabah &amp; Garcia, Filomena &amp; Knauff, Malgorzata, 2010. &quot;Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis,&quot; <em>Journal of Economic Theory</em>, 145, 1968-1986.</p>
<p>Further restrictions on the reaction functions are necessary to guarantee a symmetric equilibrium. A sufficient condition is that they are identical and linear in <span class="math-container">$y_i$</span>.</p>

CC BY-SA 4.0
2022-10-20T10:53:12.240Z
2022-10-20T10:53:12.240Z
Bertrand
<p>If a market is given to be a Cuornot duopoly and Q = q1 + q2. What assumptions can you make about q1 and q2 being equal? Is it possible for q1 &gt; q2 and thus for company 1 to have greater market share in an equilibrium?</p>
<p>Edit: I assume they have the same cost and indistinguishable products. I guess my question could be more simply boiled down to: Are they guaranteed to have inverted reaction functions?</p>

CC BY-SA 4.0
2022-10-19T02:11:55.023Z
Hint: Try solving the problem with $MC_1<MC_2$, namely, firm 1 is more efficient / has a lower marginal cost than firm 2.
Herr K.
CC BY-SA 4.0
2022-10-19T02:23:52.080Z
@HerrK. yes, oops meant to assume, that. I think I need to focus on the reaction function I am just not sure how to prove they have the same reaction function
ford prefect
CC BY-SA 4.0
2022-10-19T19:03:36.533Z
Hi, what do you mean by an *inverted* reaction function?
Rick_Morty
CC BY-SA 4.0
2022-10-21T23:25:58.737Z
@Citrus I mean would one firms reaction function necessarily be the inverse of the other firms reaction function
ford prefect
<oligopoly>
Cournot Duopoly firms guaranteed to produce the same amount
ford prefect
# Cournot Duopoly firms guaranteed to produce the same amount

(Asked by: username_0 on 2022-10-19)

If a market is given to be a Cuornot duopoly and Q = q1 + q2. What assumptions can you make about q1 and q2 being equal? Is it possible for q1 > q2 and thus for company 1 to have greater market share in an equilibrium?

Edit: I assume they have the same cost and indistinguishable products. I guess my question could be more simply boiled down to: Are they guaranteed to have inverted reaction functions?

**Tags:** oligopoly
> **Comments:**
> **username_1**: Hint: Try solving the problem with $MC_1<MC_2$, namely, firm 1 is more efficient / has a lower marginal cost than firm 2.  
> **username_0**: @HerrK. yes, oops meant to assume, that. I think I need to focus on the reaction function I am just not sure how to prove they have the same reaction function  
> **username_2**: Hi, what do you mean by an *inverted* reaction function?  
> **username_0**: @Citrus I mean would one firms reaction function necessarily be the inverse of the other firms reaction function  

---

## 1 answers

### Answer by username_3 on 2022-10-20. Score: 5 | Accepted answer

Even if firms have identical technologies and identical reaction functions, the Cournot equilibrium can be asymmetric, as shown there:

Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," *Journal of Economic Theory*, 145, 1968-1986.

Further restrictions on the reaction functions are necessary to guarantee a symmetric equilibrium. A sufficient condition is that they are identical and linear in $y\_i$.


---

