The Price of Democracy in Coalition Formation

Chalkiadakis, G., Elkind, E., Polukarov, M. and Jennings, N. R. (2009) The Price of Democracy in Coalition Formation. In: The 8th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS-2009), Budapest, Hungary, May 2009. pp. 401-408.

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Abstract

Whenever rational agents form coalitions to execute tasks, doing so via a decentralized
negotiation process—while more robust and democratic—may
lead to a loss of efficiency compared to a centralized solution. To quantify
this loss, we introduce the notion of the Price of Democracy (PoD), which
measures the amount of resources needlessly committed to the task(s) at
hand. After defining this concept for general coalitional games, we instantiate
it in the setting of weighted voting games, a simple but expressive
class of coalitional games that can be used to model resource allocation in
multiagent scenarios. We approach the problem of forming winning coalitions
in this setting from a non-cooperative perspective, and put forward an
intuitive deterministic bargaining process, which exhibits no delay of agreement
(i.e., the agents are guaranteed to form a winning coalition in round
one) and allows for efficient computation of bargaining strategies. We show
a tight bound of 3/2 on the PoD of our process if two rounds of bargaining
are allowed, and demonstrate that this bound cannot improve with more
rounds. We then generalize our bargaining process to settings where multiple
coalitions are allowed to be formed, show that this generalization also
exhibits no delay of agreement, and discuss the PoD in such settings.