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A mathematical model for a gaming community

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  • Romulus Breban

Abstract

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.

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  • Romulus Breban, 2016. "A mathematical model for a gaming community," Papers 1607.03161, arXiv.org.
    • Handle: RePEc:arx:papers:1607.03161
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    References listed on IDEAS

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    1. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    2. repec:cla:levarc:786969000000001297 is not listed on IDEAS
    3. Lehrer, Ehud & Rosenberg, Dinah, 2010. "A note on the evaluation of information in zero-sum repeated games," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 393-399, July.
    4. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    5. Valerio Capraro, 2013. "A Model of Human Cooperation in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-6, August.
    6. Zhijian Wang & Yanran Zhou & Jaimie W. Lien & Jie Zheng & Bin Xu, 2016. "Extortion Can Outperform Generosity in the Iterated Prisoners' Dilemma," Levine's Bibliography 786969000000001297, UCLA Department of Economics.
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