  In this work, we investigate the distributed generalized Nash equilibrium
(GNE) seeking problems for $N$-coalition games with inequality constraints.
First, we study the scenario where each agent in a coalition has full
information of all the constraints. A finite-time average consensus-based
approach is proposed by using full decision information. It is proven that the
algorithm converges to a GNE (specifically, a variational equilibrium) of the
game. Then, based on the finite-time consensus tracking, we propose a
distributed algorithm by using partial decision information only, where only
neighboring action information is needed for each agent. Furthermore, we
investigate the scenario where only distributive constraint information is
available for the agents. The terminology ``distributive" here refers to the
scenario where the constraint information acquisition and processing are
conducted across multiple agents in a coalition, and each agent has access to
only a subset of constraints, instead of the scenario where each agent has full
information of all the constraints. In this case, the multiplier computation
and the constraint information required for each individual are reduced. A full
decision information algorithm and a partial decision information algorithm for
this scenario are proposed, respectively. Numerical examples are given to
verify the proposed algorithms.
