图上的伊辛博弈
Ising Game on Graphs
AI总结：
本文在退火近似下分析完全图和随机图上带噪声的伊辛博弈的静态与动态均衡，发现约化伊辛博弈与完全图伊辛博弈结果一致，且静态均衡与动态稳态解的参数域重合。
摘要：
在退火近似下，分析了完全图和随机图上带噪声的二元选择（伊辛）博弈中的静态与动态均衡。考虑了两种版本：一种伊辛博弈，其相互作用项按照统计物理中的伊辛模型定义；以及一种约化伊辛博弈，其相互作用项采用图博弈论中惯常的定义。基于对外部影响的弹性考量，对塑造静态均衡模式的滞后现象进行了详细分析。写出了所考虑博弈的动态版本的福克-普朗克方程，并推导了其渐近稳态解。结果表明，对应于这些概率分布最大值的参数域与静态均衡的相应滞后区间相同。对于矩的演化方程解的局部稳定性所定义的域，也得到了相同的结果。在所有考虑的情形中，结果表明约化伊辛博弈的结果与完全图上伊辛博弈所得结果一致。对于逻辑噪声的特殊情形，伊辛博弈的静态均衡结果重现了统计物理中图上的伊辛模型的结果。
英文摘要：
Static and dynamic equilibria in noisy binary choice (Ising) games on complete and random graphs in the annealed approximation are analysed. Two versions, an Ising game with interaction term defined in accordance with the Ising model in statistical physics and a reduced Ising game with a customary definition of interaction term in game theory on graphs, are considered. A detailed analysis of hysteresis phenomenon shaping the pattern of static equilibria based on consideration of elasticity with respect to external influence is conducted. Fokker-Planck equations describing dynamic versions of the games under consideration are written and their asymptotic stationary solutions derived. It is shown that domains of parameters corresponding to the maxima of these probability distributions are identical with the corresponding hysteresis ranges for static equilibria. Same result holds for domains defining local stability of solutions of the evolution equations for the moments. In all the cases considered it is shown that the results for the reduced Ising game coincide with those obtained for the Ising game on complete graphs. It is shown that for s special case of logistic noise the results obtained for static equilibria for the Ising game reproduce those in the Ising model on graphs in statistical physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
