The emergence of new communication technologies allows us to expand our understanding of distributed control and consider collaborative decision-making paradigms. With collaborative algorithms, certain local decision-making entities (or agents) are enabled to communicate and collaborate on their actions with one another to attain better system behavior. By limiting the amount of communication, these algorithms exist somewhere between centralized and fully distributed approaches. To understand the possible benefits of this inter-agent collaboration, we model a multi-agent system as a common-interest game in which groups of agents can collaborate on their actions to jointly increase the system welfare. We specifically consider $k$-strong Nash equilibria as the emergent behavior of these systems and address how well these states approximate the system optimal, formalized by the $k$-strong price of anarchy ratio. Our main contributions are in generating tight bounds on the $k$-strong price of anarchy in finite resource allocation games as the solution to a tractable linear program. By varying $k$ --the maximum size of a collaborative coalition--we observe exactly how much performance is gained from inter-agent collaboration. To investigate further opportunities for improvement, we generate upper bounds on the maximum attainable $k$-strong price of anarchy when the agents' utility function can be designed.

翻译：新型通信技术的出现拓展了我们对分布式控制的理解，并促使我们考虑协作决策范式。通过协作算法，某些局部决策实体（或智能体）能够相互通信并就其行动进行协作，从而获得更优的系统行为。通过限制通信量，这些算法介于集中式与完全分布式方法之间。为理解智能体间协作的潜在优势，我们将多智能体系统建模为共同利益博弈，其中智能体群体可通过协作行动共同提升系统福利。我们特别将$k$-强纳什均衡视为这些系统的涌现行为，并研究这些状态逼近系统最优的程度，通过$k$-强无政府代价比率进行形式化描述。我们的主要贡献在于：针对有限资源分配博弈，通过可解线性规划给出了$k$-强无政府代价的紧界。通过改变$k$（协作联盟的最大规模），我们能够准确观测智能体间协作带来的性能提升程度。为进一步探索改进空间，当智能体效用函数可设计时，我们推导了可达$k$-强无政府代价上界。