C

In economic theories, people are typically represented as analytical agents who learn from past experiences to optimize (优化) their performance, eventually reaching a stable state in which they know how to maximise their earnings. This assumption surprised Garnier Brun at École Polytechnique in France because, as a physicist, he knew that interactions in nature such as those between atoms often result in chaos rather than stability.

I test whether economists are correct to assume that learning from the past can help people avoid chaos, Brun and his colleagues devised a mathematical mode for a game featuring hundreds of simulated players. Each player can choose between two actions, like buying or selling a stock. They also interact with each other, and the players' decision-making is influenced by what they have done before - meaning they are able to learn from experience. The researchers could adjust the precise extent to which a player's past experiences influenced their subsequent decision-making. They could also control the interactions between the players to make them either cooperate or compete with each other more.

With all these control knobs available to them, Brun and his colleagues used methods from statistical physics to simulate different game situations on a computer. In some situations, the researchers expected that the game would always result in chaos, with players unable to learn how to optimise their performance. Economic theory would also suggest that, given the right set of parameters (参数), the players would settle into a stable state where they had mastered the game - but the researchers found this wasn't really the case. The most likely outcome was a state that never settled.

Team member Jean Martin, also at École Polytechnique, says that, in the absence of one centralised and all-knowing player who could coordinate everyone, regular players could only learn how to reach "satisficing" states. That is a level that satisfied minimum expectations, but not much more. Players gained more than they would have done by playing at random, so learning wasn't useless, but they still gained less than they would have if past experience had allowed them to truly optimise their performance.

Martin says the game model is too simple to be immediately adopted for making real-world predictions, but she sees the study as a challenge to economists to drop many assumptions that currently go into theorising processes, like merchants choosing suppliers or banks setting interest rates. The finding could also be important for simulating processes like foraging decisions by animals or for some machine-learning applications, says Toby Galla at the Institute for Cross-Disciplinary Physics and Complex Systems in Spain.