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A Game of Random Variables

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  • Artem Hulko
  • Mark Whitmeyer

Abstract

This paper analyzes a simple game with $n$ players. We fix a mean, $\mu$, in the interval $[0, 1]$ and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the player whose random variable has the highest realization. We show that the position of the mean within the interval is paramount. Remarkably, if the given mean is above a crucial threshold then the unique equilibrium must contain a point mass on $1$. The cutoff is strictly decreasing in the number of players, $n$; and for fixed $\mu$, as the number of players is increased, each player places more weight on $1$ at equilibrium. We characterize the equilibrium as the number of players goes to infinity.

Suggested Citation

  • Artem Hulko & Mark Whitmeyer, 2017. "A Game of Random Variables," Papers 1712.08716, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1712.08716
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    References listed on IDEAS

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    1. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    2. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    3. Skreta, Vasiliki & Perez-Richet, Eduardo, 2017. "Information Design under Falsification," CEPR Discussion Papers 12271, C.E.P.R. Discussion Papers.
    4. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
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