## MINORITY GAME: STOCHASTIC PROCESS WITHOUT EQUILIBRIUM

### Frantisek Slanina

##### Institute of Physics, Academy of Sciences of the Czech Republic

In the series of three lectures we present the basics of the Minority Game, which was introduced in the field of econophysics in 1997 and since then it became a paradigmatic example of a frustrated evolutionary game. In the first lecture, we expose basic principles of the game, properties of its two phases and the phase transition. On the basis of numerical simulations, we show the special features of the game, which allow mapping on a Markov process and subsequent analytical solution. The solution itself is shown in the second lecture. First we explain the replica method, which is the technical tool for the solution, and then we apply it to calculate the properties of Minority Game exactly up to the critical point. The third lecture deals with extension of the Minority Game. We show how the applications come back to the field of economic phenomena, where the inspiration started. We show also another extensions which have more abstract motivations.

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