彩票的合理性评价

摘 要

本文建立1种评价标准去衡量玩各种类型彩票方案的合理性问题。而游戏规则涉及到各种因素，如各种等级奖项的中奖率、奖项、奖金额的设置以及对彩民的吸引力等。进而设计出更好的方案和相应的算法。首先，我们根据实际情况将各种彩票从整体上分类，利用全概率公式逐步剥开问题本质，得出了彩票各项具体中奖概率；基于这1结果，模型由数学期望概念得到启发，提出期望奖金解决方案，建立层次结构分析模型。通过定性比较指标层各元素的相对重要性建立对目标层的判断矩阵，得出的各个指标的权重，将评价标准彻底由抽象的表观形式转变为具体和严格的量化形式，使准确直观地比较各方案的优劣成为可能。

其次，模型运用博弈理论证明必存在1个纳什均衡，即双方利益最大化的分配方案。在这基础上，我们继而建立了主成分分析模型寻找这1纳什均衡点，将样本空间降为3维，极大地简化了问题的复杂度，结合搜索算法，简单明了地得出了问题的结论。两个模型的计算结果相差不大，充分说明了模型的合理性和稳定性。对管理部门提出合理化的建议。

关键字：层次分析法；主成分分析；博弈理论；逐步求精

Lottery Reasonable Evaluation

Author: MA Yong-ren

(College of Mathematical Sciences and Computing Technology,Tutor: MO Shang-feng

Abstract

In this paper, an evaluation criterion for playing all types of lottery programs reasonable question. And the rules of the game involving a variety of factors, such as different grades awards winners rate awards Award amount and the setting up of 100730 attractive. Then design a better program and the corresponding algorithm. First, according to the actual situation of our various lottery from the overall classification, the use of all probability formula gradually when catching nature of the problem. reached a winning lottery specific probability; Based on this result, the mathematical model from concept to be inspired expectations, Bonus expectations for solutions to establish hierarchical structure model. Qualitative indicators through more layers of the elements to establish the relative importance of the target layer judgment matrix, come to the various indicators of the weight of the evaluation criteria thoroughly apparent from the abstract into concrete form and rigorous quantitative form, enable accurate visual comparison of the pros and cons of each possible.

Secondly, the use of game theory model will prove the existence of a Nash equilibrium, that is to maximize the interests of both the distribution program. On this basis, we then established a principal component analysis model for the Nash equilibrium, sample space dimensionality reduction of 3-D, greatly simplifying the complexity of the issue, the search algorithm, simple to draw a conclusion about the issue. 2 model results are close, shows the model is reasonable and stability. Management departments to rationalize the proposals.

Keywords: AHP; Principal component analysis; Game theory; Stepwise refinement