Collaborative Coalitions in Multi-Agent Systems: Quantifying the Strong Price of Anarchy for Resource Allocation Games

TL;DR

This paper analyzes how collaboration among agents in resource allocation games affects system efficiency, providing tight bounds on the strong price of anarchy for different coalition sizes and exploring utility design improvements.

Contribution

It introduces a method to compute tight bounds on the $k$-strong price of anarchy in finite resource allocation games using linear programming, highlighting the impact of coalition size.

Findings

Tight bounds on $k$-strong price of anarchy for resource allocation games.

Performance gains increase with larger coalition sizes.

Upper bounds on maximum $k$-strong price of anarchy with utility design.

Abstract

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.