An Efficient Vector-Based Representation for Coalitional Games

We propose a new representation for coalitional games, called the coalitional skill vector model, where there is a set of skills in the system, and each agent has a skill vector—a vector consisting of values that reflect the agents’ level in different skills. Furthermore, there is a set of goals, each with requirements expressed in terms of the minimum skill level necessary to achieve the goal. Agents can form coalitions to aggregate their skills, and achieve goals otherwise unachievable. We show that this representation is fully expressive, that is, it can represent any characteristic function game. We also show that, for some interesting classes of games, our representation is significantly more compact than the classical representation, and facilitates the development of efficient algorithms to solve the coalition structure generation problem, as well as the problem of computing the core and/or the least core. We also demonstrate that by using the coalitional skill vector representation, our solver can handle up to 500 agents.