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摘要翻译：
在前驱著作《走向一个收益为概率分布的博弈理论》(ARXIV:1506.07368[Q-FIN.EC])中提出的博弈论风险管理框架在这里通过计算收益为概率分布的博弈均衡的算法细节得到了扩展。我们的方法是“数据驱动”的，因为我们假设经验数据（测量、模拟等）是可用的，可以被编译成分布模型，这些模型适合于关于偏好的有效决策，并使用这些作为收益建立和解决游戏。如果使用非参数方法（核密度估计），分布之间的偏好会变得非常简单，但使用这种模型计算博弈中的纳什均衡被发现是低效的（如果不是不可能的话）。事实上，我们给出了一个反例，在这个反例中，对于（特别是不幸的）博弈中收益分布的选择，虚拟博弈不能收敛，并引入了一个适当的收益密度的尾部近似来解决这个问题。整个过程本质上是虚拟游戏的修改版本，并在此描述用于标准和多准则游戏，以迭代地传递（近似的）纳什均衡。文中还给出了一种利用线性规划的精确方法。
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英文标题：
《On Game-Theoretic Risk Management (Part Two) -- Algorithms to Compute
Nash-Equilibria in Games with Distributions as Payoffs》
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作者：
Stefan Rass
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最新提交年份：
2020
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分类信息：
一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Computer Science 计算机科学
二级分类：Computer Science and Game Theory 计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our approach is "data driven" in the sense that we assume empirical data (measurements, simulation, etc.) to be available that can be compiled into distribution models, which are suitable for efficient decisions about preferences, and setting up and solving games using these as payoffs. While preferences among distributions turn out to be quite simple if nonparametric methods (kernel density estimates) are used, computing Nash-equilibria in games using such models is discovered as inefficient (if not impossible). In fact, we give a counterexample in which fictitious play fails to converge for the (specifically unfortunate) choice of payoff distributions in the game, and introduce a suitable tail approximation of the payoff densities to tackle the issue. The overall procedure is essentially a modified version of fictitious play, and is herein described for standard and multicriteria games, to iteratively deliver an (approximate) Nash-equilibrium. An exact method using linear programming is also given.
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PDF链接：
https://arxiv.org/pdf/1511.08591
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