Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330061 
Authors: 
Year of Publication: 
2023
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 14 [Issue:] 6 [Article No.:] 68 [Year:] 2023 [Pages:] 1-10
Publisher: 
MDPI, Basel
Abstract: 
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk 𝑋𝑛,𝑛=0,1,…} in the continuation region 𝐶:={1,2,…}, and the second player seeks to maximize the survival time in C. The process starts at 𝑋0=𝑥>0 and the game ends the first time 𝑋𝑛≤0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.
Subjects: 
random walk
first-passage time
homing problem
difference game
dynamic programming
difference equation
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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