论文标题
网络上的不对称游戏：迈向Ising-Model表示
Asymmetric games on networks: towards an Ising-model representation
论文作者
论文摘要
我们在这里研究小型网络上的性别游戏之战，这是一个不对称游戏的教科书案例。由于玩家的偏好相互矛盾，分析方法是稀缺的，并且大多数更新策略是在网络上重复游戏的数值模拟中使用的，直到达到收敛为止。结果，玩家选择之间的相关性出现。我们的方法是研究这些相关性与广义ISING模型。使用响应策略框架，我们描述了播放器的动作如何从不平衡的框架开始稳定配置。我们使用游戏理论工具获得这些配置，并使用ISING参数描述结果。我们用尽了两人案例，详细说明了所有均衡的可能性。进入三个播放器，我们概括了Ising模型，并比较了三种代表性网络的平衡解决方案。我们发现，没有直接链接的玩家保留了与最初相关性成正比的程度相关性。我们还发现，局部网络结构与磁场的小值和ISING模型的相互作用强度最相关。最后，我们得出的结论是，平衡状态的某些参数是独立于网络的，这打开了对网络上玩游戏不对称游戏的分析描述的可能性。
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.
