Please use this identifier to cite or link to this item: https://ah.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 GingYang, 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 $0-1$. 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),21-31AMS MathSciNet:MR1209488 Data Type: article Appears in Collections: [應用數學系] 期刊論文

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