A social coalitional weak equilibrium existence theorem with a continuum of agents and applications

Abstract

In this paper, we establish a social coalitional weak equilibrium existence theorem with a continuum of agents, which is an infinite-player extension of the fully cooperative version of Ichiishi (1981). As a unified approach, we obtain the weak α-core existence theorems of normal-form games and exchange economies with a continuum of agents by the social coalitional weak equilibrium existence theorem.

Keywords:

• Social coalitional weak equilibrium
• weak α-core
• existence
• a continuum of agents

2020 Mathematics Subject Classifications:

• 91A10
• 91A12
• 91A13

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This study is supported by Fundamental Research Funds for the Central Universities of China (Nos. 2020110139, 2019110312) and the Independent Scientific Research Project of Colleges for Shanghai University of Finance and Economics (Nos. 2014110323, 2021110348).