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A Discrete-Time Homing Problem with Two Optimizers

Author

Listed:
  • Mario Lefebvre

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

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.

Suggested Citation

  • Mario Lefebvre, 2023. "A Discrete-Time Homing Problem with Two Optimizers," Games, MDPI, vol. 14(6), pages 1-10, October.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:6:p:68-:d:1268507
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    References listed on IDEAS

    as
    1. Moussa Kounta & Nathan J. Dawson, 2021. "Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1155-1172, September.
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