通过变式不等式和固定点的一类新的广义纳什人口博弈

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-08-20 DOI:10.1007/s11117-024-01080-1

Yue-tian Zhan, Xue-song Li, Nan-jing Huang

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引用次数: 0

摘要

在本文中，我们提出了一类新的广义纳什-人口博弈（GNPGs），它可以用来在同一框架内捕捉人口博弈（PGs）和广义纳什博弈的理想特征。我们为 GNPG 引入了广义惯性纳什均衡（GINE）的概念，并利用变分不等式系统和定点定理的方法证明了 GINE 在紧凑和非紧凑情况下的存在性。此外，我们还引入了轻微利他的广义惯性纳什均衡（SAGINE）作为 GINE 的细化概念，并证明在一些温和的假设条件下，GNPG 至少有一个 SAGINE。

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A new class of generalized Nash-population games via variational inequalities and fixed points

In this paper, we propose a new class of generalized Nash-population games (GNPGs) which can be used to capture the desired features of both population games (PGs) and generalized Nash games within the same framework. We introduce the concept of generalized inertial Nash equilibrium (GINE) for the GNPG and show the existence of GINE by using the method of the system of variational inequalities and fixed point theorems both in the compact and noncompact cases. Moreover, we introduce a slightly altruistic generalized inertial Nash equilibrium (SAGINE) as a refinement concept of the GINE and prove that the GNPG has at least an SAGINE under some mild assumptions.

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.