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Gambler’s ruin problem on Erdős–Rényi graphs

Author

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  • Néda, Zoltán
  • Davidova, Larissa
  • Újvári, Szeréna
  • Istrate, Gabriel

Abstract

A multiagent ruin-game is studied on Erdős–Rényi type graphs. Initially the players have the same wealth. At each time step a monopolist game is played on all active links (links that connect nodes with nonzero wealth). In such a game each player puts a unit wealth in the pot and the pot is won with equal probability by one of the players. The game ends when there are no connected players such that both of them have non-zero wealth. In order to characterize the final state for dense graphs a compact formula is given for the expected number of the remaining players with non-zero wealth and the wealth distribution among these players. Theoretical predictions are given for the expected duration of the ruin game. The dynamics of the number of active players is also investigated. Validity of the theoretical predictions is investigated by Monte Carlo experiments.

Suggested Citation

  • Néda, Zoltán & Davidova, Larissa & Újvári, Szeréna & Istrate, Gabriel, 2017. "Gambler’s ruin problem on Erdős–Rényi graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 147-157.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:147-157
    DOI: 10.1016/j.physa.2016.10.056
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    1. repec:cup:cbooks:9780511771576 is not listed on IDEAS
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    3. Easley,David & Kleinberg,Jon, 2010. "Networks, Crowds, and Markets," Cambridge Books, Cambridge University Press, number 9780521195331, October.
    4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
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    Cited by:

    1. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    2. Gere, István & Kelemen, Szabolcs & Tóth, Géza & Biró, Tamás S. & Néda, Zoltán, 2021. "Wealth distribution in modern societies: Collected data and a master equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).

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