CCS22: Radical Complexity, Radicar Uncertainty Bounded Rationality - Jean-Philippe Bouchau - 2022

Title : CCS22: Radical Complexity, Radicar Uncertainty Bounded Rationality - Jean-Philippe Bouchau Author(s): Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC) Link(s) : https://www.youtube.com/watch?v=6QKyWSlgANk

Talk aims to share possible connections between complex systems and behavioural economics.

Classically, agents in economics are assumed to be rational - we ask ourselves how this could be possible in a world with unknown unknowns (some keywords: radical uncertainty, black swans etc).

(The "Wilderness" of Bounded Rationality by Sims, Sargen): There are infinitely many ways to be boundedly rational and only one way to be rational (#DOUBT).

Rationality assumes common knowledge (I know what you know, you know what I know, etc.) and unlimited computing resources. Instead, bounded rationality assumes agents go for satisficing (satisfying and sufficing) solutions.

On the other hand, a lot of systems are chaotic i.e. errors grow exponentially with time - while individual trajectories maybe unknown, their probabilities could be characterized. Complex systems complicate things further - the probabilities themselves chaotically depends on parameters/initial conditions/time (this could be a possible definition of complexity), meaning the probabilities are unknowable even if all states of world are known. As a result, we need to go to a higher level of abstraction - probabilities of probabilities. In this kind of configuration space, the optimal/quasi-optimal states are exponential in the size of the system, and are very different from one another e.g. Garnier-Bruno portfolio, showing solutions which could be labelled as satisficing.

Marginal stability is mentioned, when dynamics stop when a marginally stable, fragile state is reached. Happens when the eigenvalue spectrum \(\rho(\lambda)\) of the linear stability matrix just touches 0 - related to trade-off between efficiency and fragility. Examples include populations for ecological networks where there is a constraint that population is always positive (see R.May's bound), and in economics prices for firm networks where prices are always positive (see Hawkins-Simon condition).

A claim in economics is that learning leads to rational expectations emerging in the long run assuming a stationary environment for a sufficiently long period. However, even in some simple models it is impossible to learn, e.g. he shows a very simple 2-player game whose solution is given by the so-called Sato-Crutchfield equations - looking at the long-term behaviour for certain parameters shows that the solution has a unique fixed point, but there are also regions where there is chaos or multiple fixed points. Another example is what he calls the SK game, which is a multi-agent setting (see paper by Garnier-Brun, Benzaquen, JPB).

The fact that we don't all agree is what allows for the existence of markets.

What should we do?

• Favour possible scenarios to quantitative predictions (better to be roughly right than precisely wrong).
• Identify mechanisms at play, especially destabilizing feedback loops and systemic instabilities (Black swans may only be grey if we have the right picture of the world).
• Think of optimizing resilience, quit the optimization obsession (efficiency vs. fragility).
• Imagine precursory signals allowing one to anticipate collective effects.