From Minority Games to real markets

Abstract

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behaviour close to what is observed in real markets. In particular we find that (i) fat tails and clustered volatility arise at the phase transition point and that (ii) the crossover to random walk behaviour of prices is a finite-size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real markets, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different species of traders. This clarifies the nature of the interaction and the particular role played by the various populations.

Stylized facts of financial markets and market crashes in Minority Games

“…[10], we leave details at this level unspecified, and directly define the excess demand A(t) = N i=1 a i (t) and the payoffs of agents:…”

“…On one hand, variants of this model have been shown to reproduce quite accurately the stylized facts of financial markets [8][9][10][11]. On the other, there are analytic approaches for this model which provide exact results for the limit of infinitely many agents [12][13][14][15][16].…”

Diversity of scales makes an advantage: The case of the Minority Game

“…Thus, having this normalisation, we work on the scale of the canonical MG. We also prefer this normalisation because the calculations for the game with infinitely many groups are valid only provided I 2 g < ∞ [26].…”

“…Next, we calculate the mean free energy F using equation (26). Finally, to achieve the formula for the minima of Hamiltonian H, it suffices to carry out the following limit…”

“…Their frequencies may be broadly distributed, which induces new features into the game [23,24,25]. The case of investors with different weights was investigated for a very general setup [26]. In our work, we choose a more specific situation and show that it leads to new non-trivial consequences.…”