Complexity of coalition structure generation

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.

[1]  Deeparnab Chakrabarty,et al.  Knapsack Problems , 2008 .

[2]  Jeffrey S. Rosenschein,et al.  Coalitional skill games , 2008, AAMAS.

[3]  B. Peleg,et al.  Introduction to the Theory of Cooperative Games , 1983 .

[4]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[5]  Nicholas R. Jennings,et al.  A distributed algorithm for anytime coalition structure generation , 2010, AAMAS.

[6]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[7]  Francesco Maffioli,et al.  Approximability of hard combinatorial optimization problems: an introduction , 2000, Ann. Oper. Res..

[8]  Robert E. Tarjan,et al.  A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees , 1985, Math. Oper. Res..

[9]  Jeffrey S. Rosenschein,et al.  Power in threshold network flow games , 2009, Autonomous Agents and Multi-Agent Systems.

[10]  Xiaotie Deng,et al.  Algorithmic Cooperative Game Theory , 2008 .

[11]  Onn Shehory,et al.  Coalition structure generation with worst case guarantees , 2022 .

[12]  Julie A. Adams,et al.  Approximate Coalition Structure Generation , 2010, AAAI.

[13]  T. Matsui,et al.  A SURVEY OF ALGORITHMS FOR CALCULATING POWER INDICES OF WEIGHTED MAJORITY GAMES , 2000 .

[14]  Kyomin Jung,et al.  Coalitional Structure Generation in Skill Games , 2010, AAAI.

[15]  Daniël Paulusma,et al.  Matching Games: The Least Core and the Nucleolus , 2003, Math. Oper. Res..

[16]  Sarvapali D. Ramchurn,et al.  An Anytime Algorithm for Optimal Coalition Structure Generation , 2014, J. Artif. Intell. Res..

[17]  Vincent Conitzer,et al.  Coalition Structure Generation Utilizing Compact Characteristic Function Representations , 2009, CP.

[18]  Vincent Conitzer,et al.  Complexity of constructing solutions in the core based on synergies among coalitions , 2006, Artif. Intell..

[19]  Rahul Savani,et al.  Wiretapping a hidden network , 2009, WINE.

[20]  Sarit Kraus,et al.  On agent types in coalition formation problems , 2010, AAMAS.

[21]  Salil P. Vadhan,et al.  Computational Complexity , 2005, Encyclopedia of Cryptography and Security.

[22]  Felix Brandt,et al.  Monotone cooperative games and their threshold versions , 2010, AAMAS.

[23]  Michael Wooldridge,et al.  Computational Complexity of Weighted Threshold Games , 2007, AAAI.

[24]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[25]  Haris Aziz,et al.  Complexity of comparison of influence of players in simple games , 2008, ArXiv.