"For the past 150 years, economic theory has viewed agents in the economy (firms, consumers, investors) as perfectly rational decision makers facing well-defined problems and arriving at optimal behavior consistent with — in equilibrium with — the outcome caused by this behaviour."
The formal definition of rational actor is not nearly 150 years old. It's heyday was probably in the time of Becker, in the 70's. The study of equilibrium refinement concepts practically died before the 90's, as did General Equilibrium theory (actually before that). The straw man has seen better days.
Also, in parallel, Herb Simon started in the earnest in the 1960's and, a short time later, so did Kahneman & Tversky. Experimental and behavioral approaches, by this point, have primacy in legitimacy in all literatures where they apply.
Is it fair to converse with academic literature that is 40 or more years old - as the author does when referring to the "standard model of financial markets"? Perhaps more relevant: Is is useful?
After all, the tennet is similar to the Carnegie school around March, who already articulated all concerns the author brings to the table. However, March did so with more humility and also 50 years before the present article - arguably when the issue was more pressing.
"Complexity economics", in form of dynamic systems and chaos theory (for example) had its time in the sun, since the 70's actually, without leading to convincing new insights. Indeed I would struggle to think of any result from this literature that is as significant as Auction Theory, Behavioral Econ / Nudging, Mechanism Design & Implementation, Networks and other things that quite literally shape our daily lives (all while apparently stemming from a deficient science).
One issue with complexity as an approach is that it does not in itself get to the core problem social science faces: Agents are decision makers that can not be modeled by simplistic choice rules or analogies to physical phenomenon. The system faced by and thrust upon the actor is not independent of or impenetrable to his machinations. Every literature attempting to box human actors into the confines of behavioral laws leads nowhere - ironically a problem that representative agents and econophysics share. Such attempts, even though they pop up frequently, are always a step back. Although to be fair to the author, this is an issue he does talk about. Nevertheless, complexity economics as proposed here does not, in itself, promise to be a solution. Rather, it is an approach that equally will have to wrestle with this core issue. Perhaps then the author should acknowledge that the economist's gambit of using preferences and equilibria was an attempt, certainly an imperfect one, to face into this core issue of modeling human behavior. It is precisely not an approach ignorant of it, rather it is a reaction to it.
In any case, the straw man looms large. With his eyes open, the author would have to acknowledge that preference-based specifications and complex systems are not as different at it may seem. However, adding a diffuse element of complexity as framing to dynamic modeling and worse, co-opting other sciences such as sociology and social psychology under one's own umbrella, does not a new science make.
The heart of it is whether we wish to predict outcomes from assumed behavior, or whether we wish to characterize outcomes as consistent with agents' wants. I personally have used both approaches, but see no need to call one classical and the other complexity economics. Indeed, both coexist in a social system, they just elucidate different properties of it.
Whenever I talk to someone who flat out states that only one of the approaches has merits, then this is a person who has not read enough. The primacy of Becker is long gone. A primacy of "complexity economics" will never exist. I personally can't wait until we no longer find every discussion being framed in opposition to a now non-existent orthodoxy. I also dislike seeing approaches I personally respect being humiliated by its proponents when they show such misunderstandings of the literature.
A cynic would react differently: publishing this article in a physics journal, as opposed to addressing economists, may play to the sympathy and goodwill of physicists. Such a cynic may wonder what the author stands to gain from the inevitable applause of his non-economist peers. Especially since the same article could have been desk rejected by an economics journal with the comment: "We are keenly aware, and have been for decades, that models from the 60's have their issues".
One can voice many concerns of other points. For example, the author alludes to power laws in network diffusion, apparently unaware that research in this area has since shown that not everything that looks like a power law is in fact a power law.
Even sympathetic to the approach, I wonder whether the paper would not have deserved further revision.