Scribe Notes for ”Parameterized Complexity of Problems in Coalition Resource Games”

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. Some previous papers have shown problems in coalition games to be computationally hard. Woolbridge and Dunne [10] studied the computational complexity of several natural decision problems in Coalition Resource Games (CRGs) 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. However such hardness results consider the entire input as one and we lose out on using structural information hidden in input. In case of coalition resource games this bundles together several distinct elements of the input e.g. the agent set, the goal set, the resources etc. Shrot, Aumann and Kraus [6] examine the complexity of coalition formation problems in the CRG model as function of distinct input elements using the theory of Parameterized Complexity. Their refined analysis shows that not all parts of input act equal some instances of the problem are actually tractable.