Well-Posedness of Weakly Cooperative Equilibria for Multi-objective Population Games

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  • 1 School of Economics, Yunnan University of Finance and Economics, Kunming 650221, Yunnan, China;
    2 School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, Yunnan, China

Received date: 2023-01-20

  Revised date: 2023-11-09

  Online published: 2026-03-16

Supported by

This work was supported by the National Natural Science Foundation of China (No.11901511),the Yunnan Fundamental Research Projects (No.202101AT070216),Yunnan Provincial Department of Education (No.2022J0601),Xingdian Talents Project Foundation for Young Scholar in Yunnan Province.

Abstract

In this paper, we construct a bounded rationality function of weakly cooperative equilibrium point of multi-objective population games (WCEPOMPG) by virtue of nonlinear scalarization function. We investigate lower semicontinuity of the bounded rationality function and present a relationship between the level set of zero of the bounded rationality function and WCEPOMPG. By applying these properties, we first consider the generalized well-posedness for WCEPOMPG in the setting of multiplevalued assumption of solution set. Then, we obtain the uniqueness of solution set on a dense residual set with the stable assumption of vector payoff functions. Moreover, we investigate the well-posedness of WCEPOMPG on the dense residual set. As a special case, we obtain the generalized well-posedness and well-posedness of cooperative equilibria for single-objective population games, respectively.

Cite this article

Tao Chen, Kun-Ting Chen, Yu Zhang . Well-Posedness of Weakly Cooperative Equilibria for Multi-objective Population Games[J]. Journal of the Operations Research Society of China, 2026 , 14(1) : 293 -308 . DOI: 10.1007/s40305-023-00526-9

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