Distributed Multi-Coalition Games With General Linear Systems Over Markovian Switching Networks

In this paper, the multi-coalition game problem with incomplete information over Markovian switching networks is investigated. Each heterogeneous player involved in the problem is driven by a general linear dynamic and shares information by exploiting the randomly evolving network. All players intend to minimize the cost function of their coalition while achieving output action consensus inside the coalition. Regarding this, we develop a distributed multi-coalition game algorithm based on the proportional-integral dynamic consensus protocol. With graph theory, stochastic processes, and the stability principle, the algorithm is proven to converge exponentially to the Nash equilibrium solution, and the effect of gain parameters on the convergence rate is revealed. In addition, motivated by concerns about typical scenarios in which transition probabilities are inaccessible and the demands of the time-limited task, the discussion is extended to cases including Markovian switching networks with partly unknown transition probabilities and the formulation of a distributed predefined time scheme. Then, the corresponding analytical results are given, respectively. Finally, the effectiveness of the proposed algorithm is verified by numerical simulations.