  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.
