政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/115511

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 110097/141043 (78%)
Visitors : 46422892 Online Users : 425

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 > 社會科學學院 > 經濟學系 > 期刊論文 > Item 140.119/115511

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/115511

Title:	MAXIMIZING THE VARIANCE OF THE TIME TO RUIN IN A MULTIPLAYER GAME WITH SELECTION
Authors:	姚怡慶 GRIGORESCU, ILIE;YAO, YI-CHING
Contributors:	統計學系
Keywords:	dynamic programming;Gambler`s ruin;martingale;stochastic control
Date:	2016-06
Issue Date:	2018-01-08 11:21:45 (UTC+8)
Abstract:	We consider a game with K = 2 players, each having an integer-valued fortune. On each round, a pair (i, j) among the players with nonzero fortunes is chosen to play and the winner is decided by flipping a fair coin (independently of the process up to that time). The winner then receives a unit from the loser. All other players`fortunes remain the same. (Once a player`s fortune reaches 0, this player is out of the game.) The game continues until only one player wins all. The choices of pairs represent the control present in the problem. While it is known that the expected time to ruin (i.e. expected duration of the game) is independent of the choices of pairs (i, j) (the strategies), our objective is to find a strategy which maximizes the variance of the time to ruin. We show that the maximum variance is uniquely attained by the (optimal) strategy, which always selects a pair of players who have currently the largest fortunes. An explicit formula for the maximum value function is derived. By constructing a simple martingale, we also provide a short proof of a result of Ross (2009) that the expected time to ruin is independent of the strategies. A brief discussion of the (open) problem of minimizing the variance of the time to ruin is given.
Relation:	Advances in Applied Probability. Jun2016, Vol. 48 Issue 2, p610-630. 21p.
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1017/apr.2016.17
DOI:	10.1017/apr.2016.17
Appears in Collections:	[經濟學系] 期刊論文

Files in This Item:

File	Description	Size	Format
630.pdf		252Kb	Adobe PDF2	283	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...