An analysis of a mathematical economic game suggests that even learning from past mistakes will almost never help us optimise our decision-making – with implications for our ability to make the biggest financial gains.
When people trade stocks, they don’t always learn from experience
Even when we learn from past mistakes, we may never become optimal decision-makers. The finding comes from an analysis of a mathematical game that simulates a large economy, and suggests we may need to rethink some of the common assumptions built into existing economic theories.
In such theories, people are typically represented as rational agents who learn from past experiences to optimise their performance, eventually reaching a stable state in which they know how to maximise their earnings. This assumption surprised Jérôme 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. He and his colleagues mathematically tested whether economists are correct to assume that learning from the past can help people avoid chaos.
They devised a mathematical model for a game featuring hundreds of players. Each of these theoretical players can choose between two actions, like buying or selling a stock. They also interact with each other, and each player’s decision-making is influenced by what they have done before – meaning each player can 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, Garnier-Brun and his colleagues used methods from statistical physics to simulate different game scenarios on a computer. The researchers expected that in some scenarios 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, the virtual players would settle into a stable state where they have mastered the game – but the researchers found that this wasn’t really the case. The most likely outcome was a state that never settled.
Jean-Philippe Bouchaud at École Polytechnique, who worked on the project, says that in the absence of one centralised, omniscient, god-like player that could coordinate everyone, regular players could only learn how to reach “satisficing” states. That is, they could reach a level that satisfied minimum expectations, but not much more. Players gained more than they would have done by playing at random, so learning was not useless, but they still gained less than they would have if past experience had allowed them to truly optimise their performance.
“This work is such a powerful new way of looking at the problem of learning complex games and these questions are fundamental to the construction of models of economic decision-making,” says Tobias Galla at the Institute for Cross-Disciplinary Physics and Complex Systems in Spain. He says the finding that learning typically does not lead to outcomes better than satisficing could also be important for processes like foraging decisions by animals or for some machine learning applications.
Bouchaud says his team’s game model is too simple to be immediately adopted for making predictions about the real world, but he 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 idea that people are always making complicated economic computations and learn how to become the most rational agents, our paper invites everyone to move on [from that],” he says.
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*Credit for article given to Karmela Padavic-Callaghan*