The Game Theoretic Consensus in a Networked Multi-Agent System

Byzantine General Problem (BGP) is well known to assist robust design of distributed multi-agent systems (MAS). Although agents of wireless networking capability are common in state-of-the-art Internet of Things or cyber-physical systems, wireless networking has been hardly considered into BGP research. In this paper, we re- visit the BGP by constructing a new game theoretic framework to model agents' interactions to achieve consensus strategy by taking network topology into consideration. Then we analyze the game strategies based on incomplete information, particularly partially connected network topology that is common in a large-scale wireless network, rather than system control of fully connected network topology in traditional BGP. We further demonstrate the application of BGP to the consensus operation in a group of intelligent agents. The numerical results show that our game theoretic approach is more effective and robust in each agent's decision performance, particularly advantageous in the MAS of large-scale and partially connected network such as a platoon of autonomous driving vehicles or robots.