Game-Based Coalescence in Multi-Agent Systems
📝 Original Paper Info
- Title: Game-based coalescence over multi-agent systems- ArXiv ID: 1910.02692
- Date: 2019-10-08
- Authors: Jingying Ma, Jinming Du, and Yuanshi Zheng
📝 Abstract
Coalescence, as a kind of ubiquitous group behavior in the nature and society, means that agents, companies or other substances keep consensus in states and act as a whole. This paper considers coalescence for n rational agents with distinct initial states. Considering the rationality and intellectuality of the population, the coalescing process is described by a bimatrix game which has the unique mixed strategy Nash equilibrium solution. Since the process is not an independent stochastic process, it is difficult to analyze the coalescing process. By using the first Borel-Cantelli Lemma, we prove that all agents will coalesce into one group with probability one. Moreover, the expected coalescence time is also evaluated. For the scenario where payoff functions are power functions, we obtain the distribution and expected value of coalescence time. Finally, simulation examples are provided to validate the effectiveness of the theoretical results.💡 Summary & Analysis
This paper explores how multiple agents with different initial states can coalesce into a single group through game theory. The central issue addressed is how these diverse entities achieve consensus and act as one unit despite their varied starting points. To tackle this, the authors model the interactions between agents using bimatrix games, which are part of game theory. This approach leverages each agent's rationality and intellect to find a stable equilibrium point known as the mixed strategy Nash equilibrium. Through rigorous mathematical proof using the first Borel-Cantelli Lemma, they demonstrate that all agents will eventually coalesce into one group with probability one.The authors further evaluate the expected time for this coalescence process and derive specific distributions when payoff functions are power-based. This detailed analysis not only proves the theoretical feasibility of such a coalescence but also provides practical insights into how long it might take under different conditions. The significance of this research lies in its potential application across various domains where group behavior plays a critical role, from corporate mergers to collective decision-making processes.