Minority Game Model Research Articles

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.

Qlearning in the minority game

We present a numerical investigation of the minority game model, where the dynamics of the agents is described by the Q-learning algorithm. The numerical results show that the Q-learning dynamics is suppressing the "crowd effect," which is characteristic of the minority game with standard inductive dynamics, and it converges to a stationary state that is close to the optimal Nash equilibrium of the game.

Microscopic models for long ranged volatility correlations

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between ‘active’ and ‘inactive’ strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy, or a more sophisticated version that includes some price dynamics. We show that real market data can be surprisingly well accounted for by these simple models.

On a Universal Mechanism for Long Ranged Volatility Correlations

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between 'active' and 'inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be rather well accounted for by these simple models.

From Minority Games to real markets

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.

Social organization in the Minority Game model

We study the role of imitation within the Minority Game model of market. The players can exchange information locally, which leads to formation of groups which act as if they were single players. Coherent spatial areas of rich and poor agents result. We found that the global effectivity is optimized at certain value of the imitation probability, which decreases with increasing memory length. The social tensions are suppressed for large imitation probability, but generally the requirements of high global effectivity and low social tensions are in conflict.

Modeling market mechanism with minority game

Using the minority game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow: producers feed in the information whereas speculators make it away. How well each agent fares in the common game depends on the market conditions, as well as their sophistication. Sometimes there is much to gain with little effort, sometimes great effort virtually brings no more incremental gain. Market impact is also shown to play an important role, a strategy should be judged when it is actually used in play for its quality. Though the minority game is an extremely simplified market model, it allows to ask, analyze and answer many questions which arise in real markets.