The Simplest Unlimited-Player Game of Skill

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-03-13 DOI:10.1080/00029890.2023.2177477

B. Simon

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引用次数: 1

Abstract

Abstract The Least Unique Positive Integer game (LUPI) is among the simplest games that can be played by any number of players, N > 2, and has a nontrivial strategic component. In LUPI, players try to pick the smallest positive integer nobody else picks. Despite its simplicity, the game was not widely known until fairly recently. It was actually offered as a state run lottery game in Sweden in 2007, but players collaborated, and the game was quickly stopped. LUPI has also been proposed as the basis for a reverse auction system, and here it is proposed as a “party game”. The Nash equilibrium for the game has been previously worked out in the case where the numbers of players that make each choice are independent Poisson random variables, an assumption that can often be justified when N is large. Here we summarize previous work and derive a number of interesting new results on Nash equilibria when N is small, and when N is large using the Poisson assumption. We also investigate whether the Nash equilibrium strategies for LUPI games are evolutionary stable strategies. Finally, we look at cheating strategies for LUPI and devise ways to make it harder to cheat.

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最简单的无限玩家技能游戏

最小唯一正整数对策(LUPI)是可以由任意数量的玩家参与的最简单的对策之一，它具有非平凡的策略成分。在《LUPI》中，玩家试着选择其他人没有选择的最小的正整数。尽管它很简单，但直到最近才广为人知。它实际上是2007年在瑞典作为一种国营彩票游戏提供的，但玩家勾结，游戏很快就被停止了。LUPI也被提议作为反向拍卖系统的基础，在这里它被提议为“派对游戏”。博弈的纳什均衡之前已经在做出每个选择的玩家数量是独立泊松随机变量的情况下得到了解决，当N很大时，这个假设通常是合理的。在这里，我们总结了以前的工作，并得出了一些有趣的新结果，当N很小时，当N很大时，使用泊松假设。我们还研究了LUPI博弈的纳什均衡策略是否为进化稳定策略。最后，我们将研究LUPI的作弊策略，并设计出使其更难作弊的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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