# Deviating from Cournot-Nash

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 $x_1^*.$

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 $\epsilon>0$?

• 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 Nov 15 '17 at 7:08
• Yes I believe I understand both curves. What link between these am I failing to see? – pafnuti Nov 15 '17 at 14:01
• That is my question as well. – Giskard Nov 15 '17 at 15:59
• The link that I fail to see is whatever link implies that player $1$ benefits from deviating from $x_1^*$ – pafnuti Nov 15 '17 at 16:05
• 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 Nov 15 '17 at 16:35