一个游戏社区的数学模型
A mathematical model for a gaming community
AI总结：
研究个体在强混合下以硬币投注的零和重复博弈，发现资产分布收敛于指数分布，无论赌注大小，只要玩家永不破产。
摘要：
我们考虑一个由个体组成的大型社区，这些个体强烈混合并以对赌硬币抛掷的方式成对相遇。我们研究了参与此零和重复博弈的玩家的资产分布。我们的主要结果是，只要玩家永不破产，资产分布会收敛到指数分布，无论赌注大小。分析结果表明，指数分布是此零和重复博弈的稳定固定点，这在数值实验中得到证实。
英文摘要：
We consider a large community of individuals who mix strongly and meet in pairs to bet on a coin toss. We investigate the asset distribution of the players involved in this zero-sum repeated game. Our main result is that the asset distribution converges to the exponential distribution, irrespective of the size of the bet, as long as players can never go bankrupt. Analytical results suggests that the exponential distribution is a stable fixed point for this zero-sum repreated game. This is confirmed in numerical experiments.
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。
