网络上的非对称博弈：一种伊辛模型表示
Asymmetric games on networks: towards an Ising-model representation
摘要：
我们在这里研究的性别之战的游戏，一个教科书的情况下，不对称的游戏，在小型网络。由于冲突的球员的偏好，分析方法是稀缺的，最常见的更新策略是采用在网络上的重复游戏的数值模拟，直到收敛。结果，玩家的选择之间出现了相关性。我们的方法是研究这些相关性与广义伊辛模型。使用响应策略框架，我们描述了如何的球员的行动可以使网络进入一个稳定的配置，从一个不平衡的。我们得到这些配置使用博弈理论工具，并使用伊辛参数描述的结果。我们穷尽了两个玩家的情况，给出了所有均衡可能性的详细说明。在此基础上，我们对伊辛模型进行了推广，并对三种典型网络的均衡解进行了比较。我们发现，没有直接联系的球员保持一定程度的相关性，这是成比例的初始相关性。我们还发现，当地的网络结构是最相关的小值的磁场和相互作用强度的伊辛模型。最后，我们得出结论，某些参数的平衡态是网络无关的，这开辟了一个分析描述的不对称游戏在网络上。
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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