  This paper considers the distributed strategy design for Nash equilibrium
(NE) seeking in multi-cluster games under a partial-decision information
scenario. In the considered game, there are multiple clusters and each cluster
consists of a group of agents. A cluster is viewed as a virtual noncooperative
player that aims to minimize its local payoff function and the agents in a
cluster are the actual players that cooperate within the cluster to optimize
the payoff function of the cluster through communication via a connected graph.
In our setting, agents have only partial-decision information, that is, they
only know local information and cannot have full access to opponents'
decisions. To solve the NE seeking problem of this formulated game, a
discrete-time distributed algorithm, called distributed gradient tracking
algorithm (DGT), is devised based on the inter- and intra-communication of
clusters. In the designed algorithm, each agent is equipped with strategy
variables including its own strategy and estimates of other clusters'
strategies. With the help of a weighted Fronbenius norm and a weighted
Euclidean norm, theoretical analysis is presented to rigorously show the linear
convergence of the algorithm. Finally, a numerical example is given to
illustrate the proposed algorithm.
