少数者博弈、演化资本与复制因子动态
Minority games, evolving capitals and replicator dynamics
摘要：
我们讨论了一个简单的版本的少数者博弈（MG），其中代理人只有一个策略，但在其中他们的资本动态演变根据他们的成功，并在其中总交易量随时间相应地变化。这一特征对于MG再现真实市场数据的风格化事实至关重要。可以计算该模型的定态和相图，并且我们表明，在这个简化的模型中也存在MG常见的各态历经破相变，并且以积分响应的发散为标志。一个类似的多数博弈结果是相对缺乏有趣的特征，总资本被发现在时间上是发散的。引入一个约束力导致一个类似于进化博弈论的复制动力学模型，我们证明了在这里观察到一个不同类型的相变。最后，我们简要地讨论了这个模型的关系，每个球员一个策略，更复杂的少数人游戏的动态资本和几个交易策略，每个代理。
英文摘要：
We discuss a simple version of the Minority Game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly. This feature is known to be crucial for MGs to reproduce stylised facts of real market data. The stationary states and phase diagram of the model can be computed, and we show that the ergodicity breaking phase transition common for MGs, and marked by a divergence of the integrated response is present also in this simplified model. An analogous majority game turns out to be relatively void of interesting features, and the total capital is found to diverge in time. Introducing a restraining force leads to a model akin to replicator dynamics of evolutionary game theory, and we demonstrate that here a different type of phase transition is observed. Finally we briefly discuss the relation of this model with one strategy per player to more sophisticated Minority Games with dynamical capitals and several trading strategies per agent.
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