It's actually not primarily based on complicated mathematical assumptions, but on the simulation and also empirical data about MR!=MC in the real world. That was his primary motivation to study this problem. See Steve Keen's book Debunking Economics if you want a bit more details.

Even if you would have an endless stream of market entrants, you would also need some companies to exit, otherwise everybody would get smaller and smaller piece of the pie. In the real world, those who come will usually set the price just below the current market value. If you think about it, it's nothing else than the Keen's model with just companies being renamed endlessly (after they make one step).

But go ahead and try to simulate it, and add more realism. I think you will find very similar result (that is, profit maximizing strategy will never be to compete on price). Except for the price wars, which (in my opinion) always happen only temporarily when the big company wants to drive smaller companies out of the market entirely to get more market share as a result (just like real wars). But you need to have inelastic demand for that, otherwise I doubt it can be considered a viable strategy.

I came across Keen awhile ago, and actually made my own model of the price setting algorithm in python and confirmed his results. My beef is that it is an unrealistic constraint that the same price setting algorithm will be used by all companies. And it is possible for someone to enter the market using a different algorithm.

MR!=MC in the real world, but the classic micoecon explanation for this is monopolistic competition. I'm not sure why there is a need to say that all of economics is wrong. Are there commodities markets with open entry and no open collusion where MR!=MC? (Where marginal cost is defined as the cost of bringing on a new production line, not just producing one more unit).

Non-commodity markets get quite complicated. Often the market bifurcates into a set of premium brands and a set of low cost brands. Premium brands often try to get a monopoly over one subset of customer, who need some special feature, or try to build their brand as something special, or otherwise differentiate. Premium brands explicitly do not compete on price. Salesmen will say stuff like, "Look I know we are pricy. If you want the el cheapo software, don't buy us. Buy us if you want the good stuff."

If the market just has premium brands, that all price way above cost of production, someone is going to try to enter the market with a lower cost product.

I never gathered what point Keen was trying to make, not what he was saying that was both novel and true.

> And it is possible for someone to enter the market using a different algorithm.

By the way, I think this often happens in the real world, where some person irrationally (from the economist's point of view) provides a valuable, yet underpriced (with respect to the real demand curve) service, because he is just being misinformed, idealistic or is interested in success for its own sake, not for the sake of money. Or it's just that the product is new and actual demand curve hasn't been established yet.

Absurdly, this is then hailed as an example of market efficiency, while there is nothing rational in such behavior from the game theory perspective (unless you consider much wider frame of how human morality evolved etc.).

I think Keen makes two points. One is (as it often is the case in Debunking Economics) that this is "surprising" for students of economics. He cites various textbooks, like Mankiw. If economists know these things, why do they lie to students? It is indoctrination, plain and simple.

The second point, IIRC, is that the Cournot model of perfect competition is mathematically wrong. The assumptions that no firm can influence the price and decreasing demand curve are contradictory, regardless whether or not these provide a good model for the real world.