Complexity of coalition structure generation

TL;DR

This paper analyzes the complexity of coalition structure generation, providing polynomial-time algorithms for specific cases with bounded player types and establishing complexity results for various coalitional games.

Contribution

It introduces a general polynomial-time algorithm for coalition structure generation when player types are limited, and characterizes complexity for various compactly represented games.

Findings

Polynomial-time algorithm for games with bounded player types

Efficient algorithms for weighted voting and skill games with few weights or skills

Complexity classifications for combinatorial domain games

Abstract

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds.