The communication complexity of coalition formation among autonomous agents

It is self-evident that in numerous Multiagent settings, selfish agents stand to benefit from cooperating by forming coalitions. Nevertheless, negotiating a stable distribution of the payoff among agents may prove challenging. The issue of coalition formation has been investigated extensively in the field of cooperative n-person game theory, but until recently little attention has been given to the complications that arise when the players are software agents. The bounded rationality of such agents has motivated researchers to study the computational complexity of the aforementioned problems. In this paper, we examine the communication complexity of coalition formation, in an environment where each of the n agents knows only its own initial resources and utility function. Specifically, we give a tight ⊖(n) bound on the communication complexity of the following solution concepts in unrestricted games: Shapley value, the nucleolus and the modified nucleolus, equal excess theory, and the core. Moreover, we show that in some intuitively appealing restricted games the communication complexity is constant, suggesting that it is possible to achieve sublinear complexity by constraining the environment or choosing a suitable solution concept.