摘要翻译：
我们在这里研究两性之战游戏，一个在小型网络上的非对称游戏的教科书案例。由于博弈者偏好的冲突，分析方法很少，通常在网络上重复博弈的数值模拟中使用更新策略，直到达到收敛。结果，玩家的选择之间出现了相关性。我们的方法是用一个广义的伊辛模型来研究这些相关性。利用响应策略框架，我们描述了参与者的行为如何使网络从非均衡状态进入稳定状态。我们利用博弈论工具得到这些构型，并用伊辛参数描述结果。我们穷尽了两人情形，给出了所有均衡可能性的详细说明。针对三个参与者，我们推广了Ising模型，并比较了三种典型网络的均衡解。我们发现，没有直接联系的参与者保留了一个与其初始相关性成正比的关联度。我们还发现局域网络结构与小磁场值和Ising模型的相互作用强度最相关。最后，我们得出了均衡状态的某些参数与网络无关的结论，这为分析描述网络上的非对称博弈提供了可能性。
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英文标题：
《Asymmetric games on networks: towards an Ising-model representation》
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作者：
A. D. Correia, L. L. Leestmaker and H. T. C. Stoof
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最新提交年份：
2021
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分类信息：

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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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model. Using the response strategy framework, we describe how the actions of the players can bring the network into a steady configuration, starting from an out-of-equilibrium one. We obtain these configurations using game-theoretical tools, and describe the results using Ising parameters. We exhaust the two-player case, giving a detailed account of all the equilibrium possibilities. Going to three players, we generalize the Ising model and compare the equilibrium solutions of three representative types of network. We find that players that are not directly linked retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. Finally, we conclude that certain parameters of the equilibrium states are network independent, which opens up the possibility of an analytical description of asymmetric games played on networks.
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