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彩票的合理性評(píng)價(jià)
摘 要
本文建立1種評(píng)價(jià)標(biāo)準(zhǔn)去衡量玩各種類型彩票方案的合理性問(wèn)題。而游戲規(guī)則涉及到各種因素，如各種等級(jí)獎(jiǎng)項(xiàng)的中獎(jiǎng)率、獎(jiǎng)項(xiàng)、獎(jiǎng)金額的設(shè)置以及對(duì)彩民的吸引力等。進(jìn)而設(shè)計(jì)出更好的方案和相應(yīng)的算法。首先，我們根據(jù)實(shí)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(kāi)問(wèn)題本質(zhì)，得出了彩票各項(xiàng)具體中獎(jiǎng)概率；基于這1結(jié)果，模型由數(shù)學(xué)期望概念得到啟發(fā)，提出期望獎(jiǎng)金解決方案，建立層次結(jié)構(gòu)分析模型。通過(guò)定性比較指標(biāo)層各元素的相對(duì)重要性建立對(duì)目標(biāo)層的判斷矩陣，得出的各個(gè)指標(biāo)的權(quán)重，將評(píng)價(jià)標(biāo)準(zhǔn)徹底由抽象的表觀形式轉(zhuǎn)變?yōu)榫唧w和嚴(yán)格的量化形式，使準(zhǔn)確直觀地比較各方案的優(yōu)劣成為可能。
其次，模型運(yùn)用博弈理論證明必存在1個(gè)納什均衡，即雙方利益最大化的分配方案。在這基礎(chǔ)上，我們繼而建立了主成分分析模型尋找這1納什均衡點(diǎn)，將樣本空間降為3維，極大地簡(jiǎn)化了問(wèn)題的復(fù)雜度，結(jié)合搜索算法，簡(jiǎn)單明了地得出了問(wèn)題的結(jié)論。兩個(gè)模型的計(jì)算結(jié)果相差不大，充分說(shuō)明了模型的合理性和穩(wěn)定性。對(duì)管理部門提出合理化的建議。
關(guān)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
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