### The Minority Game

The El Farol restaurant in Santa Fe has "one of the best bars on earth" according to the New York Times. Unfortunately, on the days when it becomes too crowded it's more fun to stay at home. This can be modelled by a game known as the El Farol Bar Game or its simpler cousin, the Minority Game.

In the Minority Game, N players (with N odd) get to cast a secret vote either for A or for B. When all the votes have been cast the winners are the members of the minority group and they receive a payoff. But what is surprising about this game isn't just the game itself but the people who are studying it - physicists. The idea is that for large N the game looks like certain types of system from statistical thermodynamics. For example, consider the Ising model. In this we have an array of atoms, each of which can be spin up or spin down. Depending on the parameters of the model atoms either want to be aligned like their neighbours or aligned in the opposite direction. In the latter case we have a situation similar to the Minority Game. The Minority Game looks a lot like a 'frustrated' physical system with no obvious ground state. Just as a group start moving towards what seems like the optimum it ceases to be an optimum.

The game has been studied by many people using computer simulations. Typically the simulations result in the number of winners in each round hovering around one value. But the feature that many researchers have found interesting is the way that over multiple plays, independent players seem to spontaneously cooperate, despite the lack of communication. The result is that they reduce the variance, and hence risk, of the outcome below what you would expect from a purely randomised strategy.

MG can be used to model a wide variety of phenomena besides Saturday night drinking - including financial markets, traffic congestion, network congestion and even the ebb and flow of fashion.

The original paper by Mallet and Zhang may be found here but a web search will reveal that there are in fact hundreds of papers on the subject. It seems to be the

In the Minority Game, N players (with N odd) get to cast a secret vote either for A or for B. When all the votes have been cast the winners are the members of the minority group and they receive a payoff. But what is surprising about this game isn't just the game itself but the people who are studying it - physicists. The idea is that for large N the game looks like certain types of system from statistical thermodynamics. For example, consider the Ising model. In this we have an array of atoms, each of which can be spin up or spin down. Depending on the parameters of the model atoms either want to be aligned like their neighbours or aligned in the opposite direction. In the latter case we have a situation similar to the Minority Game. The Minority Game looks a lot like a 'frustrated' physical system with no obvious ground state. Just as a group start moving towards what seems like the optimum it ceases to be an optimum.

The game has been studied by many people using computer simulations. Typically the simulations result in the number of winners in each round hovering around one value. But the feature that many researchers have found interesting is the way that over multiple plays, independent players seem to spontaneously cooperate, despite the lack of communication. The result is that they reduce the variance, and hence risk, of the outcome below what you would expect from a purely randomised strategy.

MG can be used to model a wide variety of phenomena besides Saturday night drinking - including financial markets, traffic congestion, network congestion and even the ebb and flow of fashion.

The original paper by Mallet and Zhang may be found here but a web search will reveal that there are in fact hundreds of papers on the subject. It seems to be the

*in*thing.Labels: mathematics

## 2 Comments:

It seems to be the in thing.That's a fantastically ironic end statement.

Korollary,

It seemes you detected a faint trace of the paragraph I wrote and then deleted on the grounds that maybe it was a bit too cynical. :-)

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