摘要翻译：
本文综合研究了有效制度下少数人博弈的效用函数。我们开发了一个有效的游戏状态描述。对于收益函数$g(x)=\sgn(x)$,我们将博弈显式表示为马尔可夫过程，并证明了状态数的有限性。我们还证明了效用函数的有界性。利用这些事实，我们可以解释总需求的所有有趣的可观察的特征：强烈波动的出现、它们的周期性和偏好水平的存在。对于另一个收益$g(x)=x$，状态的数目仍然是有限的，效用仍然是有界的，但是状态的数目不能减少，状态的概率也不计算。然而，利用效用的性质和用德布鲁因图分析博弈，我们也可以解释不同的需求峰值及其频率。
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英文标题：
《Phenomenology of minority games in efficient regime》
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作者：
Karol Wawrzyniak and Wojciech Wislicki
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Adaptation and Self-Organizing Systems        自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=\sgn (x)$ we explicitly represent the game as the Markov process and prove the finitness of number of states. We also demonstrate boundedness of the utility function. Using these facts we can explain all interesting observable features of the aggregated demand: appearance of strong fluctuations, their periodicity and existence of prefered levels. For another payoff, $g(x)=x$, the number of states is still finite and utility remains bounded but the number of states cannot be reduced and probabilities of states are not calculated. However, using properties of the utility and analysing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies.
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PDF链接：
https://arxiv.org/pdf/0907.3231