Stylized facts and wealth inequality in zero-sum mixed-strategy minority game

Abstract

In this work, we introduce two modifications in the minority game with dynamic capitals: (1) mixed strategies where the agents avoid their worst performing strategy and favor but not necessarily choose their best performing strategy; and (2) zero-sum game in which the total gain of the minority group is equal to the total loss of the majority group. The phase transitions in the volatility versus length of memory of the standard minority game are similarly observed in the minority game with mixed strategies. We find in the zero-sum minority game with dynamic capitals that stylized facts, such as long-range volatility correlations and "fat tails" in the distribution of the absolute returns, occur in the efficient regime of the game (short memory). This observation is attributed to the nature of the mixed strategies used by the agents. On the other hand, the time series of the Gini index, used to characterize wealth inequality among the agents, are found to saturate to approximately the same value anywhere in the regime of the minority game with the zero-sum capital redistribution.