Thank you very much, Professor Ping, for your valuable contribution to the debate.

There are further complications due to the need for subsequent decision-making by the entities and its effects, but compared to the scale of how this subject begins, they are small.

Dear Greg,
Thank you very much for your interesting comments on my paper. I will try to answer your questions.
1.- The relationship between complexity and prediction is not a simple one. For instance, see Mihailovic et al. (2014) at https://www.hindawi.com/journals/amete/2014/878249/
2.- I think you´re right in your argument on the relationship between your interesting paper and Robert and Yoguel´s criteria.
3.- I´m not a philosopher, so I presume you have a better answer to questions 4 and 5. What I want to underline is that multiple equilibria implies that the result attained is path-dependent. History matters.
Thank you for the references in point 5. I will read them with interest and benefit.

1. I’m interested in agents who do more than optimize, and I’m interested in the role that ideas and theories play in decision making. However, your point about the difficulty in building models to study areas like economics where most of the data is of the low frequency variety is a good one. I did, however, come across Robert Shiller’s 2017 AEA Presidential Address on “Narrative Economics,” which uses Google searches to trace the “rise and fall” of different ideas (memes?) over time. These can be simple narratives, such as “don’t wait until you’re priced out of the housing market,” or more complicated theories like the so-called “Laffer Curve,” which played a big role in the justifying the tax cuts of the Reagan and Thatcher administrations.

2. You point out that Richard Day (1994) says, “An economic system is dynamically complex if its deterministic endogenous processes do not lead it asymptotically to a fixed point, a limit cycle, or an explosion.” Can this be roughly translated as saying, “An economic system is dynamically complex if its future ‘path’ cannot be predicted”? Does this mean it has no equilibria? (Apologies if these are silly questions).

3. Don’t know if this is of interest to anyone besides me, but my paper (for this conference) seems to match up with 3 or 4 of the 5 summary criteria of complexity put forward by Robert and Yoguel’s (2013): i) “heterogeneity, ii) disequilibrium and divergence, iii) interactions and partial information iv) network architecture, and v) emergent properties.” I have i) autonomous agents with ii) multiple beliefs, who iii) interact in many institutions and environments on the basis of diverse beliefs, which produces iv) some kind of disequilibrium, if only in the form of disappointed expectations.

4. You write, “The multiplicity of equilibria means that there are many possible worlds.” A philosophical question for you: Are all these worlds made of the same basic stuff or can they be made of different “materials,” e.g., different concepts? This isn’t a well-formed question.

5. You write, “From this perspective, the economy can be seen as a process of self-organization: the system ‘chooses’ between the different options that are presented to it.” I don’t think you mean that the “system,” itself, is an agent, but rather are employing something like Daniel Dennett’s “intentional stance.” The danger in this is well-described by the Wittgensteinian philosopher, P.M.S. Hacker, in a number of books, but especially in The Philosophical Foundations of Neuroscience, where Hacker argues that you make decisions, your brain doesn’t. You can Google to find Dennett and John Searle’s side of the argument if you’re interested.

Thanks for sharing your article. There’s a lot more in it that bears comment, but you’ve certainly got me thinking.