政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/120128

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 113311/144292 (79%)
Visitors : 50941316 Online Users : 946

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer

政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/120128

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/120128

Title:	On the ""fair`` games problem for the weighted generalized Petersburg games
Authors:	林光賢 Lin, Kuang Hsien 陳天進 Chen, Ten Ging Yang, Ling-Huey
Contributors:	應數系
Date:	1993-03
Issue Date:	2018-09-25 16:22:01 (UTC+8)
Abstract:	Let $S_n=\\sum^n_{j=1}a_jY_j$, $n\\geq 1$, where $\\{Y_n,\\ n\\geq 1\\}$ is a sequence of i.i.d. random variables with the generalized Petersburg distribution $P\\{Y_1=q^{-k}\\}=pq^{k-1}$, $k\\geq 1$, where $0<p=1-q<1$ and $a_n,\\ n\\geq 1$, are positive constants with $(\\sum^n_{j=1}a_j)/\\max_{1\\leq j\\leq n}a_j\\to\\infty$. The main result asserts that $S_n/M_n\\overset P\\to\\rightarrow 1$, where $$M_n=\\sup\\Big\\{x\\colon\\ \\sum^n_{j=1}a_jEY_1I(a_jY_1\\leq x)\\geq x\\Big\\},\\quad n\\geq 1,$$ thereby generalizing a result of A. Adler and the reviewer [Bull. Inst. Math. Acad. Sinica 17 (1989), no. 3, 211–227; MR1042179] obtained for the particular choice $a_n=n^\\alpha$, $n\\geq 1$, where $\\alpha>-1$. This problem has the following interesting interpretation. Suppose a player wins $a_nY_n$ dollars during the $n$th game in a sequence of generalized Petersburg games. If $M_n=\\sum^n_{j=1}m_j$ represents the accumulated entrance fees for playing the first $n$ games, then $S_n/M_n\\overset P\\to\\rightarrow 1$ is the assertation that $\\{m_n,\\ n\\geq 1\\}$ is a "fair solution in the weak sense to the games``.
Relation:	Chinese Journal of Mathematics,21(1),21-31 AMS MathSciNet:MR1209488
Data Type:	article
Appears in Collections:	[應用數學系] 期刊論文

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML2	292	View/Open

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

Loading...