The minority game with different payoff functions: crowd–anticrowd theory

The crowd–anticrowd theory is applied to explain the features observed in a class of the minority game using different payoff functions. Simulations results using both the full strategy space and a reduced strategy space reveal that the standard deviation (SD) in the number of agents making a particular decision over time as a function of the agents’ memory size m does not depend on the explicit form of the payoff function. The robustness of the results is explained in terms of the general features in strategy selection among the agents in different regimes of m. While different payoff functions may affect the popularity of a particular strategy, the strategy selection is found to be insensitive to the choice of payoff functions. The crowd–anticrowd cancellation effect leads to a minimum in SD at an intermediate value of m separating the small m regime characterized by crowd behavior and the large m regime characterized by random coin-toss behavior of the agents.