Research On The Coalescence Problem Of Multi-agent Systems Based On Game Theory

Due to the widespread application of multi-agent systems in fields such as information,biology,and social sciences,they have attracted great interest from scholars in the control community.This paper uses mathematical tools such as matrix theory,game theory,and probability theory to study the coalescence behavior in multi-agent systems.Coalescence refers to the process of isolated individuals or particles merging into a single entity.This paper considers the coalescence problem in multi-agent systems with incomplete information individuals.The main research contents of this paper are as follows:1.Coalescence problem of multi-agent systems when there are agents with incomplete information and no learning ability.As these agents lack learning ability,their strategies remain unchanged.In this case,the article first models the interaction between agents as a bi-matrix game and studies the game strategies of agents with complete information.Furthermore,the game strategies of agents with complete information are studied,obtaining sufficient conditions for the aggregation of multi-agent systems and proving that the final aggregation state is located within the convex hull formed by the initial states of the agents.Finally,four simulation examples are provided to verify the correctness of the theoretical results.2.Coalescence problem of multi-agent systems when agents with incomplete information have learning ability.Firstly,this article analyzes the learning patterns of agents with incomplete information and the process of evolving into agents with complete information through learning.It is proved that agents with incomplete information that have learning ability can evolve into agents with complete information after a finite number of games.Then,this article compares the coalescence time of multi-agent systems composed of agents with incomplete information that have learning ability with those that do not.When the game mechanism tends to promote cooperation between agents,it is found that systems composed of agents with incomplete information that have a learning mechanism have higher coalescence efficiency and shorter average coalescence time.Simulation examples are provided to verify the correctness of the theoretical results.In summary,the coalescence of multi-agent systems for above two cases are mainly studied.