Distributed Variational Equilibrium Seeking of Multi-coalition Game via Variational Inequality Approach

This paper studies the distributed variational equilibrium seeking problem for a class of multi-coalition non-cooperative games via a continuous-time algorithm. In the multi-coalition game, there are multiple coalitions and each coalition (a virtual player in the game) is composed of a set of agents, which are actual decision makers for their coalition and cooperate to minimize the coalition payoff function. To solve this problem, the variational equilibrium seeking problem for a multi-coalition game is first formulated as a distributed variational inequality problem. Then, a novel distributed projected continuous-time algorithm, which is in the form of a projected ordinary differential equation, is proposed to solve the distributed variational inequality. Finally, the algorithm is applied to a numerical example to show the efficacy of the proposed algorithm.