摘要翻译：
我们调查具有不同持续时间的活动。我们将利润强度定义为这一经济范畴的度量。对于一类广泛的随机反向交易（即平仓）概率分布，重复交易中的利润强度具有一个独特的性质，即无论需求曲线的形状如何，在一个固定点处达到最大值。这种类型的市场博弈在研究中经常被考虑，目的是寻找一种算法，使一个与世界其他地方谈判价格的交易者（一个集体对手）的利润最大化，这个交易者拥有一个明确和客观的供应概况。这种理想化忽视了单个交易者对世界其他地区的需求/供应状况的有时重要影响，在极端情况下，对需求/供应状况的概念提出了质疑。因此，我们提出了一个交易模型，在这个模型中，世界其他地区的需求/供给状况促使（理性的）交易者（主观地）假设他/她除了平均交易频率之外，几乎没有关于市场的所有知识。这一观点将最大熵原理引入到模型中，拓宽了可视为热力学系统的经济现象的范围。因此，利润强度有一个不动点：当交易概率按黄金比率规则$\frac{\sqrt{5}-1}{2}$给定时，强度上的利润达到最大值。
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英文标题：
《A model of subjective supply-demand: the maximum Boltzmann/Shannon
  entropy solution》
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作者：
Edward W. Piotrowski and Jan Sladkowski
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最新提交年份：
2008
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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：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transaction (ie closing of the position). This type of market games is often considered in the research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent) that posses a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/hers average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economics phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point:the profit in tensity reaches its maximum when the probability of transaction is given by the Golden Ratio rule $\frac{\sqrt{5}-1}{2}$.
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PDF链接：
https://arxiv.org/pdf/0811.2084