Parameterized Complexity of Problems in Coalitional Resource Games
Rajesh Chitnis, MohammadTaghi Hajiaghayi, Vahid Liaghat

TL;DR
This paper investigates the parameterized complexity of decision problems in coalitional resource games, establishing hardness results and fixed-parameter tractability for various problem parameters.
Contribution
It answers an open question by proving W[1]-hardness of the SC problem when parameterized by coalition size and extends complexity analysis to related resource problems.
Findings
SC problem is W[1]-hard when parameterized by coalition size
Various resource-related problems are W[1]-hard or co-W[1]-hard with respect to coalition size
Some problems are fixed-parameter tractable when parameterized by goal set size or combined agent and resource set sizes
Abstract
Coalition formation is a key topic in multi-agent systems. Coalitions enable agents to achieve goals that they may not have been able to achieve on their own. Previous work has shown problems in coalitional games to be computationally hard. Wooldridge and Dunne (Artificial Intelligence 2006) studied the classical computational complexity of several natural decision problems in Coalitional Resource Games (CRG) - games in which each agent is endowed with a set of resources and coalitions can bring about a set of goals if they are collectively endowed with the necessary amount of resources. The input of coalitional resource games bundles together several elements, e.g., the agent set Ag, the goal set G, the resource set R, etc. Shrot, Aumann and Kraus (AAMAS 2009) examine coalition formation problems in the CRG model using the theory of Parameterized Complexity. Their refined analysis…
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Taxonomy
TopicsGame Theory and Voting Systems · Logic, Reasoning, and Knowledge · Complexity and Algorithms in Graphs
