论文标题
动力学方法的渐近行为，用于集体动态的岩石剪辑二进制游戏
Asymptotic behaviors of a kinetic approach to the collective dynamics of a rock-paper-scissors binary game
论文作者
论文摘要
本文研究了由非局部和非线性集成差异方程给出的度量设置，研究了岩纸仪二进制游戏的动力学动力学。在证明了方程式的良好性之后，我们提供了大时对渐近行为的精确描述。为此，我们采用了双重性方法，这既适合按半群的平均值来构建度量解决方案的第一步，并获得渐近措施的明确表达。甚至认为方程是非线性的，此措施也可以线性地取决于初始条件。该结果是由总变化规范中的衰减完成的，由于方程的非线性，该结果恰好是子几形。这取决于对应用Harris型定理所需的限制条件的异常使用，该条件是从最近的论文[2]中获取的，该论文也提供了一种明确计算上述衰减中涉及常数的方法。
This article studies the kinetic dynamics of the rock-paper-scissors binary game in a measure setting given by a non local and non linear integrodifferential equation. After proving the wellposedness of the equation, we provide a precise description of the asymptotic behavior in large time. To do so we adopt a duality approach, which is well suited both as a first step to construct a measure solution by mean of semigroups and to obtain an explicit expression of the asymptotic measure. Even thought the equation is non linear, this measure depends linearly on the initial condition. This result is completed by a decay in total variation norm, which happens to be subgeometric due to the nonlinearity of the equation. This relies on an unusual use of a confining condition that is needed to apply a Harris-type theorem, taken from a recent paper [2] that also provides a way to compute explicitly the constants involved in the aforementioned decay in norm.
