The coalition structure generation problem is one of the key challenges in multi-agent coalition formation. It involves partitioning a set of agents into coalitions so that system performance is optimized. To date, the multi-agent systems literature has focused exclusively on the utilitarian version of this problem which seeks to maximize the sum of the values of the coalitions involved. However, there are many examples of situations in which other performance metrics are of interest. In particular, in games with non-transferable utility, we may be more interested in an egalitarian optimal coalition structure, or in minimizing the difference between the utilities of the most affluent and poorest agents. In this paper, we present a number of exact algorithms to solve such non-utilitarian formulations of the coalition structure generation problem.

We consider the issue of representing coalitional games in multi-agent systems with externalities (i.e., in systems where the performance of one coalition may be affected by other co-existing coalitions). In addition to the conventional partition function game representation (PFG), we propose a number of new representations based on a new notion of externalities. In contrast to conventional game theory, our new concept is not related to the process by which the coalitions are formed, but rather to the effect that each coalition may have on the entire system and vice versa. We show that the new representations are fully expressive and, for many classes of games, more concise than the conventional PFG. Building upon these new representations, we propose a number of approaches to solve the coalition structure generation problem in systems with externalities. We show that, if externalities are characterised by various degrees of regularity, the new representations allow us to adapt coalition structure generation algorithms that were originally designed for domains with no externalities, so that they can be used when externalities are present. Finally, building upon Rahwan et al. [16] and Michalak et al. [9], we present a unified method to solve the coalition structure generation problem in any system, with or without externalities, provided sufficient information is available.

The authors are grateful for financial support received from the UK EP-SRC through the project Market-Based Control of Complex Computational Systems (GR/T10657/01). The authors are also thankful to Jennifer McManus, School of English, University of Liverpool for excellent editorial assistance.