Anytime Coalition Structure Generation with Worst Case Guarantees

TL;DR

This paper introduces an anytime algorithm for coalition structure generation that guarantees a tight bound on optimality with minimal search, outperforming existing methods and adaptable to distributed, strategic settings.

Contribution

It presents a novel algorithm that guarantees a tight bound with minimal search, establishing a lower bound on the necessary search effort for coalition structure generation.

Findings

The algorithm guarantees a tight bound within minimal search effort.

Searching one additional node halves the bound.

The fraction of nodes searched approaches zero as agents increase.

Abstract

Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.