  Distributed Nash equilibrium (NE) seeking problem for multi-coalition games
has attracted increasing attention in recent years, but the research mainly
focuses on the case without agreement demand within coalitions. This paper
considers a class of networked games among multiple coalitions where each
coalition contains multiple agents that cooperate to minimize the sum of their
costs, subject to the demand of reaching an agreement on their state values.
Furthermore, the underlying network topology among the agents does not need to
be balanced. To achieve the goal of NE seeking within such a context, two
estimates are constructed for each agent, namely, an estimate of partial
derivatives of the cost function and an estimate of global state values, based
on which, an iterative state updating law is elaborately designed. Linear
convergence of the proposed algorithm is demonstrated. It is shown that the
consistency-constrained multi-coalition games investigated in this paper put
the well-studied networked games among individual players and distributed
optimization in a unified framework, and the proposed algorithm can easily
degenerate into solutions to these problems.
