有和无分数折扣的球面巨典范少数对策
Spherical grand-canonical minority games with and without score discounting
摘要：
我们提出了一个球形版本的巨正则少数博弈（GCMG），并解决其动力学在稳态。该模型显示了多个遍历阶段和一个非遍历阶段之间的几种类型的过渡。我们推导出解析解，包括精确表达式的波动率，在所有遍历阶段，并计算系统的相行为。与传统的GCMG相比，其中引入记忆损失排除了分析方法，当考虑指数贴现时，球形模型也可以求解。对于同质激励交易的情况下，记忆损失率ρ，一个有效的阶段，只有当ρ = ρ =0。允许异构的记忆丧失率，我们发现，只要有任何有限的分数代理，这是不受记忆丧失的效率可以实现。
英文摘要：
We present a spherical version of the grand-canonical minority game (GCMG), and solve its dynamics in the stationary state. The model displays several types of transitions between multiple ergodic phases and one non-ergodic phase. We derive analytical solutions, including exact expressions for the volatility, throughout all ergodic phases, and compute the phase behaviour of the system. In contrast to conventional GCMGs, where the introduction of memory-loss precludes analytical approaches, the spherical model can be solved also when exponential discounting is taken into account. For the case of homogeneous incentives to trade epsilon and memory loss rates rho, an efficient phase is found only if rho=epsilon=0. Allowing for heterogeneous memory-loss rates we find that efficiency can be achieved as long as there is any finite fraction of agents which is not subject to memory loss.
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