Score-dependent payoffs and Minority Games

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 distribution of the returns. Furthermore, the score-dependent payoffs could coexist with the inactive strategy in the grand canonical MG, and play an important role in the thermal MG.