JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering

Accepted manuscript available online (unedited version)

Analysis of the Pareto equilibrium in multi-objective games using semi-tensor product

Author(s): Fanyueyang ZHANG, Jun ′ e FENG ^‡
Affiliation(s): School of Mathematics, Shandong University, Jinan 250100, Shandong, China
Corresponding email(s): fengjune@sdu.edu.cn
Key Words: Multi-objective game; Pareto equilibrium; Semi-tensor product; Finite-step reachability; Finite-step controllability

Share this article to： More <<< Previous Paper \|Next Paper >>>

Fanyueyang ZHANG, Jun ′ e FENG ^‡. Analysis of the Pareto equilibrium in multi-objective games using semi-tensor product[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.2400945

@article{title="Analysis of the Pareto equilibrium in multi-objective games using semi-tensor product",
author="Fanyueyang ZHANG, Jun ′ e FENG ^‡",
journal="Frontiers of Information Technology & Electronic Engineering",
year="in press",
publisher="Zhejiang University Press & Springer",
doi="https://doi.org/10.1631/FITEE.2400945"
}

%0 Journal Article
%T Analysis of the Pareto equilibrium in multi-objective games using semi-tensor product
%A Fanyueyang ZHANG
%A Jun ′ e FENG ^‡
%J Frontiers of Information Technology & Electronic Engineering
%P 1222-1236
%@ 2095-9184
%D in press
%I Zhejiang University Press & Springer
doi="https://doi.org/10.1631/FITEE.2400945"

TY - JOUR
T1 - Analysis of the Pareto equilibrium in multi-objective games using semi-tensor product
A1 - Fanyueyang ZHANG
A1 - Jun ′ e FENG ^‡
J0 - Frontiers of Information Technology & Electronic Engineering
SP - 1222
EP - 1236
%@ 2095-9184
Y1 - in press
PB - Zhejiang University Press & Springer
ER -
doi="https://doi.org/10.1631/FITEE.2400945"

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: Multi-objective games (MOGs) have received much attention in recent years as a class of games with vector payoffs. Based on the semi-tensor product (STP), this paper discusses the MOG, including the existence, finite-step reachability, and finite-step controllability of Pareto equilibrium of this model, from both static and dynamic perspectives. First, the MOG concept is presented using multi-layer graphs, and STP is used to convert the payoff function into its algebraic form. Then, from the static perspective, two necessary and sufficient conditions are proposed to verify whether all players can meet their expectations and whether the strategy profile is a Pareto equilibrium, separately. Furthermore, from the dynamic perspective, a strategy updating rule is designed to investigate the finite-step reachability of the evolutionary MOG. Finally, the finite-step controllability of the evolutionary MOG is analyzed by adding pseudo-players, and a backward search algorithm is provided to find the shortest evolutionary process and control sequence.

利用半张量积分析多目标博弈中的Pareto均衡

张樊悦阳，冯俊娥
山东大学数学学院，中国济南市，250100
摘要：近年来受到广泛关注的多目标博弈（MOG）是一类具有向量收益的博弈。本文基于半张量积（STP），从静态和动态两个角度讨论该MOG模型的Pareto均衡存在性、有限步可达性和有限步可控性。首先，利用多层图提出MOG的概念，并利用STP将收益函数转化为代数形式。然后，从静态角度分别提出验证所有玩家是否都能满足其期望和验证局势是否为Pareto均衡的两个充分必要条件。进而，从动态角度设计策略更新规则来研究演化MOG的有限步可达性。最后，通过添加伪玩家分析演化MOG的有限步可控性，并给出一种寻找最短演化过程和控制序列的反向搜索算法。

关键词组：多目标博弈；Pareto均衡；半张量积；有限步可达性；有限步可控性

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

Open peer comments: Debate/Discuss/Question/Opinion

<1>

- Go to

利用半张量积分析多目标博弈中的Pareto均衡

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference