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

On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information