<p>Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that in a sequential game, player $1$ benefits from deviating (upwards) from $x_1^*.$</p>

<p><a href="https://i.sstatic.net/8P3qn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8P3qn.png" alt="enter image description here"></a></p>

<p>The isoprofit curve maps the level of $x_1$ onto $x_2$ such that each combination 
generates player $1$'s Cournot equilibrium profit $\pi^*$.</p>

<p>How exactly does this diagram show that player $1$ benefits by player $x_1+\epsilon$, where $\epsilon&gt;0$?</p>

CC BY-SA 3.0
2017-11-15T07:08:39.107Z
Your exact problem is unclear. Do you understand what an Isoprofit Curve is? Do you understand what a Reaction Function is? If yes, what exactly causes your confusion?
Giskard
CC BY-SA 3.0
2017-11-15T14:01:28.487Z
Yes I believe I understand both curves. What link between these am I failing to see?
pafnuti
CC BY-SA 3.0
2017-11-15T15:59:45.717Z
That is my question as well.
Giskard
CC BY-SA 3.0
2017-11-15T16:05:30.873Z
The link that I fail to see is whatever link implies that player $1$ benefits from deviating from $x_1^*$
pafnuti
CC BY-SA 3.0
2017-11-15T16:35:58.053Z
His move $x_1 + \epsilon$ and the corresponding response from player 2 is higher on the Isoprofit Curve than $x_1$ and the corresponding response from player 2.
Giskard
<microeconomics><mathematical-economics><game-theory><nash-equilibrium>
Deviating from Cournot-Nash
pafnuti
# Deviating from Cournot-Nash

(Asked by: username_0 on 2017-11-15)

Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x\_1$ and $x\_2$. The Cournot equilibrium is $x\_1^\*,x\_2^\*$. The following diagram purports to show that in a sequential game, player $1$ benefits from deviating (upwards) from $x\_1^\*.$

[![enter image description here](https://i.sstatic.net/8P3qn.png)](https://i.sstatic.net/8P3qn.png)

The isoprofit curve maps the level of $x\_1$ onto $x\_2$ such that each combination
generates player $1$'s Cournot equilibrium profit $\pi^\*$.

How exactly does this diagram show that player $1$ benefits by player $x\_1+\epsilon$, where $\epsilon>0$?

**Tags:** microeconomics, mathematical-economics, game-theory, nash-equilibrium

> **Comments:**
> **username_1**: Your exact problem is unclear. Do you understand what an Isoprofit Curve is? Do you understand what a Reaction Function is? If yes, what exactly causes your confusion?  
> **username_0**: Yes I believe I understand both curves. What link between these am I failing to see?  
> **username_1**: That is my question as well.  
> **username_0**: The link that I fail to see is whatever link implies that player $1$ benefits from deviating from $x_1^*$  
> **username_1**: His move $x_1 + \epsilon$ and the corresponding response from player 2 is higher on the Isoprofit Curve than $x_1$ and the corresponding response from player 2.  

---

## 0 answers

