Payoffs which depend on the scores of the strategies are introduced into the standard Minority Game (MG). The double-periodicity behavior of the standard model is consequently removed, and stylized facts arise, such as long-range volatility correlations and “fat-tails” of the probability...

A dynamic herding model with interactions of trading volumes is introduced. At time t, an agent trades with a probability, which depends on the ratio of the total trading volume at time t−1 to its own trading volume at its last trade. The price return is determined by the volume imbalance and...