You yourself talk about the possibility of the emergence of complex structures from simple individual behaviors.
In other words, you acknowledge that it is the individual behaviors that are necessary for the complex structures to exist. There may not be a simple linear relationship between the individual action and the ultimate outcome, but that doesn't change the fact that individual actions have an influence on the market price.
It also doesn't change the fact that without individual actions, a market price would never change (and would never exist in the first place), and that therefore, individuals have some power over the market price.
That does not mean that an individual can just dictate what the price should be without any constraints, but it does mean that your definition of a competitive market is a meaningless phantasy that cannot possibly exist.
The whole field of optimal control theory is about how to control complex structures that emerge from individual controls.
Edit to add: By the way, outside of the theoretical argument, I think it's a good idea to take a brief look at what kind of markets exist empirically. In all markets that actually exist, it is obvious that there are actors who are capable of changing the market price.
This holds for exchanges, where actors change the price by buying or selling. It also holds for more everyday markets where it's typically the seller who puts up a sticker price. For example, the people running a supermarket set the price for the items in the supermarket.
One last thought: My argument is basically that for every market, there is some function f whose outputs are the prices in the market, and that the only inputs of this function is the history of actions of market participants (the shape of the function depends on the structure of the market).
My argument then continues to say that since the market price is a function of only the actions of the market participants, there must be at least one market participant whose actions influence the price, otherwise the price could never change. This is a simple mathematical statement.
Your attempted counter-argument is that the function f could be very complicated, which is completely irrelevant to my argument.
