具有内积策略定义的少数者对策的生成函数分析
Generating functional analysis of minority games with inner product strategy definitions
摘要：
我们使用生成函数的方法来解决所谓的内积版本的少数人游戏（MG），假和/或真实的市场历史，通过推广最近开发的理论与真实的历史查找表MG。查找表和内积MG版本的相图通常被发现是相同的，除了其中历史被线性采样的内积MG之外，其被发现是结构临界的。然而，我们遇到有趣的差异，在理论（其中的历史频率分布的作用，在查找表MG的历史协方差矩阵的本征值谱的内积MG）和静态和动态现象的模型。我们的理论预测得到了数值模拟的支持。
英文摘要：
We use generating functional methods to solve the so-called inner product versions of the minority game (MG), with fake and/or real market histories, by generalizing the theory developed recently for look-up table MGs with real histories. The phase diagrams of the lookup table and inner product MG versions are generally found to be identical, with the exception of inner product MGs where histories are sampled linearly, which are found to be structurally critical. However, we encounter interesting differences both in the theory (where the role of the history frequency distribution in lookup table MGs is taken over by the eigenvalue spectrum of a history covariance matrix in inner product MGs) and in the static and dynamic phenomenology of the models. Our theoretical predictions are supported by numerical simulations.
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