A Distributed Proximal-Gradient Based Algorithm for N-Coalition Games of Mixed-Order Players

This brief investigates the N-coalition games of mixed-order players, where first and second-order integrator-type players interact in the coalitions. Every player is associated with a nonsmooth cost function, and the objective of each coalition is to minimize its cost function which is the sum of local cost functions of the players. That is, the mixed-order players within the coalition collaboratively minimize their coalition’s cost function. To seek the Nash equilibrium of the N-coalition game, a distributed proximal-gradient based algorithm is proposed, where the proximal operator is used to deal with the nonsmoothness of the cost functions. The convergence of the proposed algorithm is analyzed by Lyapunov stability theorem. An example of mobile sensor networks is given to verify the effectiveness of the algorithm.