Interpretation of Nash equilibrium as a potential stable point of a dynamic process
I am not a big fan of any &quot;dynamic adjustment&quot; ideas in static games to justify Nash equilibrium, but for some people it is helpful. I would see it more as an inner monologue with many &quot;what if&quot;-questions.
As an example, consider Cournot competition. Supposse, two firms compete in quantities. The figure below (also from the wikipedia page) depicts the reaction functions (or best-response functions). If firm 2 sets quantity $q_2$, the best response by firm 1 is to set $q_1= R1(q_2)$. We have a Nash equilibrium where these two functions intersect, i.e., when all firms play a best response against each other. The NE is at $(q1,q2)$ in the figure.

Suppose firm 1 thinks: &quot;I believe firm 2 sets quantity $q'_2&lt;q2$. Hence, I will respond with $q'_1=R1(q'_2)$.&quot; Next firm 1 would think: &quot;But wait, if I set $q'_1$, then firm 2 would not set $q'_2$, but $q''_2=R2(q'_1)$. This means I should set $q''_1=R1(q''_2)$.&quot; Next: &quot;But wait, then firm 2 would set $q'''_2=R2(q''_1)$...&quot; and so on. This though process converges to the NE $(q1,q2)$. Similarly, we arrive at the same NE when starting with $q'_2&gt;q2$. If you want to, you can also think about the firms actually setting these quantities in repeated interactions, making only one of the steps of the thought experiment, and thereby they would also arrive at the NE and stay there.
In this sense,  &quot;a Nash equilibrium can also be interpreted as a potential stable point of a dynamic adjustment process in which individuals adjust their behavior to that of the other players in the game, searching for strategy choices that will give them better results.&quot;