摘 要
本文建立1種評價標準去衡量玩各種型別彩票方案的合理性問題。而遊戲規則涉及到各種因素，如各種等級獎項的中獎率、獎項、獎金額的設定以及對彩民的吸引力等。進而設計出更好的方案和相應的演算法。首先，我們根據實際情況將各種彩票從整體上分類，利用全概率公式逐步剝開問題本質，得出了彩票各項具體中獎概率；基於這1結果，模型由數學期望概念得到啟發，提出期望獎金解決方案，建立層次結構分析模型。通過定性比較指標層各元素的相對重要性建立對目標層的判斷矩陣，得出的各個指標的'權重，將評價標準徹底由抽象的表觀形式轉變為具體和嚴格的量化形式，使準確直觀地比較各方案的優劣成為可能。
其次，模型運用博弈理論證明必存在1個納什均衡，即雙方利益最大化的分配方案。在這基礎上，我們繼而建立了主成分分析模型尋找這1納什均衡點，將樣本空間降為3維，極大地簡化了問題的複雜度，結合搜尋演算法，簡單明瞭地得出了問題的結論。兩個模型的計算結果相差不大，充分說明了模型的合理性和穩定性。對管理部門提出合理化的建議。
關鍵字：層次分析法；主成分分析；博弈理論；逐步求精
Lottery Reasonable Evaluation
Author: MA Yong-ren
(College of Mathematical Sciences and Computing Technology,
Hunan University of Science and Technology, Xiangtan 411201, China)
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