Explicit equilibria in a kinetic model of gambling.
Explicit equilibria in a kinetic model of gambling.
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DOI：
10.1103/physreve.81.066115
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
Federico Bassetti;Giuseppe Toscani
中科院分区：
文献类型：
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作者：
Federico Bassetti;Giuseppe Toscani
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，在均匀分布的随机分数的情况下，指数分布表现为稳态，而Gamma分布则表现为Beta分布的随机分数。赌博游戏的情况下，只有保守的平均值，导致一个明确的重尾分布。
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, the exponential 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.