Distributed Resource Allocation Over Multiple Interacting Coalitions: A Game-Theoretic Approach

Despite the fact that many distributed resource allocation (DRA) algorithms have been reported in the literature, it is still unknown how to allocate resources optimally over multiple interacting coalitions. One major challenge in solving such a problem is that the relevance of one coalition's decision to other coalitions' benefits may lead to conflicts of interest among these coalitions. Within this context, a new game model is formulated in the present note, termed as resource allocation game, where each coalition contains multiple agents cooperating to maximize the coalition-level benefit subject to an intracoalition resource constraint described by a coupled equality. Inspired by techniques such as variable replacement, gradient tracking, and leader-following consensus, a new DRA algorithm is developed. It is shown that the proposed algorithm converges linearly to the Nash equilibrium (NE) of the proposed game while satisfying the resource constraint during the whole NE-seeking process. Finally, the effectiveness of the proposed allocation algorithm is verified by numerical simulations.