电磁平衡博弈：概率论视角
The Electromagnetic Balance Game: A Probabilistic Perspective
摘要：
使用天平（通常是双臂天平）从一组视觉上相同的硬币中找到重量不同的假币，称为平衡问题，是一个有趣和鼓舞人心的问题。它的变体涉及各种各样的工具包，包括信息论，编码理论，优化，概率论，组合学和许多机智。在本文中，一些变种的平衡游戏进行了讨论，特别是从概率的角度。与重力场的设置不同，我们采用了电磁场，在这里可以找到更严格的平衡游戏的一些变体的边界。我们专注于预定的设置，玩家必须在不观察平衡结果的情况下安排策略。通过采用编码方案，得到了平衡获胜的充分条件。除了设计一个精致的编码框架，我们还提出并分析了一个完全随机化的策略的性能。导出了随机局中人的最优行为。然后，我们提出了不诚实的平衡博弈，在这个博弈中，平衡可以对参与者进行不利的欺骗。最后给出了用概率方法分析不诚实平衡博弈的一些初步结果。在噪声信道中，它与香农编码定理的关系也被揭示出来。
英文摘要：
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve diversified toolkits including information theory, coding theory, optimization, probabilistic theory, combinatorics and a lot of quick wits. In this paper some variants of the balance game are dicussed, especially from a probabilistic perspective. Unlike the gravity field setting, we adopt an electromagnetic field, where tighter bounds for some variants of the balance game can be found. We focus on the predetermined setting, where the player has to arrange the strategy without observing the outcome of the balancing. The sufficient condition for the balance to win is obtained by adopting a coding scheme. Apart from designing a delicate encoding framework, we also propose and analyze the performance of a completely randomized strategy. The optimal behavior of a randomized player is derived. Then we rise the dishonest balance game, in which the balance can adversely cheat the player. We present some elementary results on the analysis of dishonest balance game using probabilistic method at length. Its relationship with Shannon' s coding theorem in a noisy channel is also revealed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
