DRAG: Distributed Resource Allocation Games over Multiple Interacting Coalitions

TL;DR

This paper introduces a novel multi-coalition game model for distributed resource allocation, proposing algorithms that ensure convergence to Nash equilibrium while respecting resource constraints, validated through simulations.

Contribution

It formulates a new multi-coalition game model and develops two algorithms for distributed resource allocation with proven linear convergence to Nash equilibrium.

Findings

Algorithms converge linearly to Nash equilibrium.

Resource constraints are maintained throughout the process.

Validation through numerical simulations confirms effectiveness.

Abstract

Despite many distributed resource allocation (DRA) algorithms have been reported in literature, it is still unknown how to allocate the resource optimally over multiple interacting coalitions. One major challenge in solving such a problem is that, the relevance of the decision on resource allocation in a coalition to the benefit of others may lead to conflicts of interest among these coalitions. Under this context, a new type of multi-coalition game is formulated in this paper, termed as resource allocation game, where each coalition contains multiple agents that cooperate to maximize the coalition-level benefit while subject to the resource constraint described by a coupled equality. Inspired by techniques such as variable replacement, gradient tracking and leader-following consensus, two new kinds of DRA algorithms are developed respectively for the scenarios where the individual benefit of each agent explicitly depends on the states of itself and some agents in other coalitions, and on the states of all the game participants. It is shown that the proposed algorithms can converge linearly to the Nash equilibrium (NE) of the multi-coalition game while satisfying the resource constraint during the whole NE-seeking process. Finally, the validity of the present allocation algorithms is verified by numerical simulations.