<p>In the book <a href="http://link.springer.com/book/10.1007/978-3-540-24792-0" rel="nofollow noreferrer">Sushko, I. (Ed.). (2002). Oligopoly dynamics: Models and tools. Springer.</a></p>

<p>there is a chapter,</p>

<p><a href="http://link.springer.com/chapter/10.1007/978-3-540-24792-0_5" rel="nofollow noreferrer">Puu, T., Gardini, L., &amp; Sushko, I. (2002). Cournot duopoly with kinked demand according to Palander and Wald. (pp. 111-146). </a></p>

<p>where the authors examine in detail a specific numerical example, among other variants.  They arrive at the best response functions and find that there exists two Cournot equilibria, for which, as they write</p>

<blockquote>
  <p><em>"...both equilibria, the Cournot points, are locally stable. They hence coexist with each its proper basin of attraction in the space of
  initial conditions."</em></p>
</blockquote>

<p>The authors are concerned with dynamics, hence the mention of "initial conditions". If one wanted to turn their conclusions into the static case with just one move to equilibrium, one should consider in which "basin of attraction" does the zero output vector belongs.</p>

CC BY-SA 3.0
2017-03-31T18:53:22.623Z
2017-03-31T18:53:22.623Z
Alecos Papadopoulos
<p>Do you know if there exist results for Cournot oligopoly (or duopoly) when the inverse demand is a piecewise continuous?
Something of this type </p>

<ul>
<li>$P(Q) = \alpha-\beta Q$ (if $0\leq Q&lt;Q'$)  </li>
<li>$P(Q) = \gamma-\delta Q$ (if $Q' \leq Q \leq Q_{max}$)</li>
</ul>

CC BY-SA 3.0
2017-03-31T08:23:13.430Z
What exactly do you mean by 'results'? Results as in published academic papers?
Giskard
<microeconomics><industrial-organisation>
Cournot model with piecewise inverse demand
Matteo Sereno
# Cournot model with piecewise inverse demand

(Asked by: username_0 on 2017-03-31)

Do you know if there exist results for Cournot oligopoly (or duopoly) when the inverse demand is a piecewise continuous?
Something of this type

* $P(Q) = \alpha-\beta Q$ (if $0\leq Q* $P(Q) = \gamma-\delta Q$ (if $Q' \leq Q \leq Q\_{max}$)

**Tags:** microeconomics, industrial-organisation
> **Comments:**
> **username_1**: What exactly do you mean by 'results'? Results as in published academic papers?  

---

## 1 answers

### Answer by username_2 on 2017-03-31. Score: 1

In the book [Sushko, I. (Ed.). (2002). Oligopoly dynamics: Models and tools. Springer.](http://link.springer.com/book/10.1007/978-3-540-24792-0)

there is a chapter,

[Puu, T., Gardini, L., & Sushko, I. (2002). Cournot duopoly with kinked demand according to Palander and Wald. (pp. 111-146).](http://link.springer.com/chapter/10.1007/978-3-540-24792-0_5)

where the authors examine in detail a specific numerical example, among other variants. They arrive at the best response functions and find that there exists two Cournot equilibria, for which, as they write

> *"...both equilibria, the Cournot points, are locally stable. They hence coexist with each its proper basin of attraction in the space of
> initial conditions."*

The authors are concerned with dynamics, hence the mention of "initial conditions". If one wanted to turn their conclusions into the static case with just one move to equilibrium, one should consider in which "basin of attraction" does the zero output vector belongs.


---

