When does the concept of equilibrium work in economics?

This looks very naive and dated already.

Basic, undergrad economics textbooks are very simplistic and most discussion is based on models with unique equilibrium and no uncertainty involved.

But serious economics is full of results on models with multiple equilibria, uncertainty, dynamics, games and what a whole lot of market imperfections.

It is common to see people from other areas (specially STEM) to take the naive textbook econ as the state of the art and make critiques that where long addressed...

Steve Keen does some interesting work modelling economies as complex dynamic systems (I think basically not really ever being in a state of equilibrium). He even got grants to create a new systems dynamics application for that purpose [1] (really ugly UI though unfortunately).

I believe he (and others) contend that the idea of an economy being in equilibrium was really only mostly a simplifying assumption that early economists made because it made things easier to calculate, but doesn't really reflect reality. It just along the way got turned into an economic "law" accidentally along the way in the history of economics.

1. https://sourceforge.net/projects/minsky/

This article seems to be written with the assumption that there is always a unique equilibrium. In most interesting instances, there are many. However, a set of cognitive limitations seems to cause people to focus on models with a unique equilibrium solution (e.g. Prisoners Dilemma) rather than more interesting models (e.g. Game of Chicken, coordination games etc)

In addition, people seem like to confuse the economic meaning of rationality (optimization subject to constraints) with their fantasies of what "rational" means). They like this confusion so much that more well known cases are considered worth of a Nobel.

If you are honestly interested in understanding the role equilibria play in economics, don't overload the term. Think of an equilibrium as a prediction of where behavior tends accepting the idea that which equilibrium is selected can depend on expectations. In that regard, Karl Shell's seminal work on Sunspot Equilibria is very informative.

As for rationality, ask if the following make sense: People make choices from subsets of a vector space. They can choose between any two elements of such a vector space. Given `N` elements of such a vector space, if x1 is better than x2 and x2 is better than x3 and ... x(N-1) is better than xN, then xN is NOT better than x1. Given any element X of the choice space, one can imagine another element Y which is close to X but is better than X.

By the way, the last one, local nonsatiation, is what people tend to call "greed".

If those assumptions make sense, then you don't have much of a problem with rational choice theory.

In particular, if those assumptions make sense, you accept that demand curves are downward sloping.

I was interested about exactly what economic theories could be dislodged by this so I read the paper and... the article isn't particularly representative.

The major finding send to be that learning algorithms are good at playing best-reply games, even though learning algos are based on memory but may have imperfect knowledge of the game and rules, while best-reply requires no memory but perfect understanding.

As I understand it, they use that to find a strong inverse correlation in best-reply games between probability of finding equilibrium and complexity (or range of action), but barely mention economics in the paper.

I think it is a fair point to make that economics relies a fair bit on the concept of the equilibrium, a fact that may be historically grown. Equilibria and how they arise were discussed long before the concept was formalized. On the other hand, at least in describing macro-system, one was interested to find simplified analogies to physical systems. Yet, equilibria also arise from the behavioral assumptions we place on micro-behavior. As such, I think it is difficult to give only one reason as to why equilibria are used so often. At the very least, each econ model needs to content with the question whether the equilibrium of the system is a relevant concept to analyse.

What I think is not fair assertion, and the article is especially full of hype, is that there has no reflection. Herbert Simon introduced bounded rationality in 1947 or earlier. This is the conception of when agents may not act rational (ie. collectively seek equilibria) because they do not understand the game sufficiently. This is not far later in time from when the equilbrium, as we know it today, emerged in the literature.

The article presents a narrative where economists do not understand these bounds, and the authors are the first to do experiments on whether people find equilibria, when in truth this has been going on almost since Nash. The whole field of behavioral economics exists... More intricate formal equilibria concepts, as opposed to behavioral and experimental analysis, have not been en-vogue since the 1980s!

Similarly, the (formal) question whether behavior of agents can converge to an equilibrium, whether it is unique, and how fast this happens, is intimately related to the whole literature. The exact question of myopic best replies, for example, was certainly formally tackled in the 80's, (Milgrom and Roberts, I think), if not before.

At the very least, it seems that the article was not peer reviewed sufficiently.

But this is very common with econophysics. Their solution, however, to get rid of strategic interaction and instead consider people as myopic, non strategic particle-like beings to be described by complex, yet non-interdependent functions, has to this day not yielded any appreciable advances in understanding economic issues - at least in the micro field.

In contrast, game theory, mechanism design and auction theory have been tremendously successful in describing certain interactions. At least they are what drivers much of the online business today, as one example. The key is, by the way, not only how well people understand the game, but also whether the interaction is indeed anonymous or more socially complex. But again, this is old news.

If you're interested in this topic you might like:

- Why markets fail (https://www.amazon.com/How-Markets-Fail-Economic-Calamities/...)

- Thinking in Systems (https://www.amazon.com/Thinking-Systems-Donella-H-Meadows-eb...)

"Modeling stock return distributions with a quantum harmonic oscillator" (2018) https://iopscience.iop.org/article/10.1209/0295-5075/120/380...

> We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features "quantized" eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

"Quantum harmonic oscillator" https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

Well worth reading on this topic is a book called "The Alchemy of Finance"[0] by one of the most successful investors in history, George Soros (successful like "made a billion dollars in a day" successful).

Soros contends, and I tend to agree with him, that the concept of equilibrium is a complete farce, is not supported by the evidence, and has no relevance to the way markets operate.

A good way to determine the conviction of economists (especially academic ones) with respect to any theory of equilibrium which they may have is to ask them if they have risked personal capital in situations to prove their theories (ie: if equilibrium is real, then why wouldn't you bet on it). The answer tends not to be yes.

[0]: https://www.amazon.com/Alchemy-Finance-George-Soros/dp/04714...

the start of the monopoly game

If anyone is interested in this sort of thing, I'd highly recommend the (very technical) book Why Stock Markets Crash by Didier Sornette - a guy who comes from a Physics/Geophysics background.

tl;dr - Stock markets crash because of fractals/chaos/complex systems. And there's no such thing as an equilibrium (in the stock market) because if there was, everyone would agree on the true value of a stock and no one would buy or sell for that reason.