  We are concerned with a distributed approach to solve multi-cluster games
arising in multi-agent systems. In such games, agents are separated into
distinct clusters. The agents belonging to the same cluster cooperate with each
other to achieve a common cluster goal while a non-cooperative game is played
between the clusters. To be able to deal with the sparsity of information, as
each agent only knows a specific part of the problem, we combine
gradient-tracking and consensus methods for information distribution into an
algorithm that can solve both the cooperative and non-cooperative problem in a
single run. The constraints of the problem are taken into account by the
corresponding projection operators and linear convergence is proven given an
appropriate constant step size. The algorithm is applied to a day-ahead power
management problem, posed as a multi-cluster game, and its efficiency is
demonstrated by simulations.
