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Abstract: Adaptive populations such as those in financial markets and distributedcontrol can be modeled by the Minority Game. We consider how their dynamicsdepends on the agents- initial preferences of strategies, when the agents uselinear or quadratic payoff functions to evaluate their strategies. We find thatthe fluctuations of the population making certain decisions the volatilitydepends on the diversity of the distribution of the initial preferences ofstrategies. When the diversity decreases, more agents tend to adapt theirstrategies together. In systems with linear payoffs, this results in dynamicaltransitions from vanishing volatility to a non-vanishing one. For low signaldimensions, the dynamical transitions for the different signals do not takeplace at the same critical diversity. Rather, a cascade of dynamicaltransitions takes place when the diversity is reduced. In contrast, no phasetransitions are found in systems with the quadratic payoffs. Instead, a basinboundary of attraction separates two groups of samples in the space of theagents- decisions. Initial states inside this boundary converge to smallvolatility, while those outside diverge to a large one. Furthermore, when thepreference distribution becomes more polarized, the dynamics becomes moreerratic. All the above results are supported by good agreement betweensimulations and theory.



Autor: H. M. Yang, Y. S. Ting, K. Y. Michael Wong

Fuente: https://arxiv.org/







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