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A Game of Nontransitive Dice

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  • Artem Hulko
  • Mark Whitmeyer

Abstract

We consider a two player simultaneous-move game where the two players each select any permissible $n$-sided die for a fixed integer $n$. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for $n>3$, there is a unique Nash Equilibrium in pure strategies. The unique Nash Equilibrium is for each player to throw the Standard $n$-sided die, where each side has a different number. Our proof of uniqueness is constructive. We introduce an algorithm with which, for any nonstandard die, we may generate another die that beats it.

Suggested Citation

  • Artem Hulko & Mark Whitmeyer, 2017. "A Game of Nontransitive Dice," Papers 1706.00849, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1706.00849
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    File URL: http://arxiv.org/pdf/1706.00849
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