Non-equilibrium statistical mechanics of endogenous fluctuations in systems of heterogeneous interacting agents

Minority game can be regarded as an Ising Model for system of heterogeneous adaptive agents, who interact through a global mechanism which involves competition for limited resources as in financial markets, for this reason it can be qualifies as a complex systems. Markets are institutions which allow agents to exchange goods. Through these exchanges, traders can reallocate their resources in order to increase their profit. Since trading itself does not create wealth, the market must be a zero sum game. Taking out transaction costs and other frictions which are needed to reward the market maker for the service he is providing, the game becomes a Minority Game. Comparing real financial market with the Minority Game it is obvious that the latter cannot describe the complexity of the former in all its conditions and regimes, but the Minority Game can be considered a faithful picture of a financial market. The key observation is that the Minority Game is tailored to study fluctuation phenomena and their statistical properties. Statistical physics suggests that the collective behavior of a system of many interacting units, is qualitatively rather indifferent to microscopic details. Stock market prices are characterized by anomalous collective fluctuations which are strongly reminiscent of critical phenomena.The connection with critical phenomena is natural, because financial markets are indeed complex systems of many interacting degrees of freedom, the traders. Minority Games provide a natural microscopic explanation for the volatility correlations found in real markets. Hence the Minority Game offers a broad picture of how financial markets operate, consistent with empirical data.