Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System

TL;DR

This paper introduces a decentralized game-theoretical framework for task allocation in large multi-agent systems, ensuring convergence to stable solutions efficiently and robustly in dynamic environments.

Contribution

It presents a novel autonomous decision-making algorithm that guarantees convergence to Nash stability using local interactions, with analytical bounds on suboptimality.

Findings

Algorithm guarantees convergence within polynomial time

Framework is scalable and adaptable to dynamic environments

Achieves at least 50% suboptimality bound under certain conditions

Abstract

This paper proposes a novel game-theoretical autonomous decision-making framework to address a task allocation problem for a swarm of multiple agents. We consider cooperation of self-interested agents, and show that our proposed decentralized algorithm guarantees convergence of agents with social inhibition to a Nash stable partition (i.e., social agreement) within polynomial time. The algorithm is simple and executable based on local interactions with neighbor agents under a strongly-connected communication network and even in asynchronous environments. We analytically present a mathematical formulation for computing the lower bound of suboptimality of the solution, and additionally show that 50% of suboptimality can be at least guaranteed if social utilities are non-decreasing functions with respect to the number of co-working agents. The results of numerical experiments confirm that the proposed framework is scalable, fast adaptable against dynamical environments, and robust even in a realistic situation.