A Discrete-Time Homing Problem with Two Optimizers

Mario Lefebvre ()
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Mario Lefebvre: Department of Mathematics and Industrial Engineering, Polytechnique Montréal, 2500, Chemin de Polytechnique, Montréal, QC H3T 1J4, Canada

Games, 2023, vol. 14, issue 6, 1-10

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 { X n , 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 X 0 = x > 0 and the game ends the first time X n ≤ 0 . An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.

Keywords: random walk; first-passage time; homing problem; difference game; dynamic programming; difference equation (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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