一类赌博动力学模型的显式平衡
Explicit equilibria in a kinetic model of gambling
摘要：
我们介绍并讨论了一个非线性动力学方程的玻尔兹曼型描述财富的演化在一个纯粹的赌博过程中，两个代理的财富的总和是赌博，并随机共享的代理之间。对于这个方程的分析形式的稳定状态的各种实现的随机分数的总和是共享的代理。其中，吉布斯分布在均匀分布的随机分数的情况下表现为稳态，而伽马分布则表现为贝塔分布的随机分数。在这种情况下，赌博游戏是唯一的保守的平均值，导致一个明确的重尾分布。
英文摘要：
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, Gibbs distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.
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