A Discrete-Time Homing Problem with Two Optimizers

IF 0.6 Q4 ECONOMICS

Games Pub Date : 2023-10-27 DOI:10.3390/g14060068

Mario Lefebvre

引用次数: 0

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.

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具有两个优化器的离散时间寻的问题

考虑一个随机差分博弈，其中一个参与者希望最小化在连续区域C:={1,2，…}中的可控一维对称随机游走{Xn,n=0,1，…}所花费的时间，第二个参与者寻求最大化C中的生存时间。该过程从X0=x>0开始，游戏在第一次Xn≤0时结束。导出了值函数的精确表达式，并由此得到了最优解，明确地求解了具体问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Games Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

11 weeks

期刊介绍： Games (ISSN 2073-4336) is an international, peer-reviewed, quick-refereeing open access journal (free for readers), which provides an advanced forum for studies related to strategic interaction, game theory and its applications, and decision making. The aim is to provide an interdisciplinary forum for all behavioral sciences and related fields, including economics, psychology, political science, mathematics, computer science, and biology (including animal behavior). To guarantee a rapid refereeing and editorial process, Games follows standard publication practices in the natural sciences.