Discrete-time stopping games with risk-sensitive discounted cost criterion

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2024-07-02 DOI:10.1007/s00186-024-00864-1

Wenzhao Zhang, Congying Liu

引用次数: 0

Abstract

In this paper, we focus on the discrete-time stopping games under the risk-sensitive discounted cost criterion. The state space and the action spaces of all the players are assumed to be Borel spaces. The cost functions are allowed to be unbounded from above and from below. At each decision epoch, each player chooses an action to influence the transition laws, and player 1 incurs a running cost. If players 1 or 2 decides to stop the game, player 1 incurs a corresponding terminated cost. Under suitable hypothesis, we show that the game model has a value which is a unique solution of risk-sensitive stopping optimality equation by an approximation technique. Furthermore, we derive the existence of equilibria.

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具有风险敏感贴现成本标准的离散时间停止博弈

本文主要研究风险敏感贴现成本准则下的离散时间停止博弈。假设所有博弈者的状态空间和行动空间都是 Borel 空间。成本函数允许自上而下无约束。在每个决策时段，每个参与者都会选择一个行动来影响过渡规律，参与者 1 会产生运行成本。如果玩家 1 或 2 决定停止博弈，则玩家 1 会产生相应的终止成本。在合适的假设条件下，我们通过近似技术证明了博弈模型有一个值是风险敏感停止最优方程的唯一解。此外，我们还推导出了均衡的存在性。

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

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.