On the complexity of cooperative solution concepts
Mathematics of Operations Research
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Computing the Banzhaf power index in network flow games
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Honor among thieves: collusion in multi-unit auctions
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
PRIMA'11 Proceedings of the 14th international conference on Agents in Principle, Agents in Practice
Handling negative value rules in MC-net-based coalition structure generation
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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Coalitional games raise a number of important questions from the point of view of computer science, key among them being how to represent such games compactly, and how to efficiently compute solution concepts assuming such representations. Marginal contribution nets (MC-nets), introduced by Ieong and Shoham, are one of the simplest and most influential representation schemes for coalitional games. MC-nets are a rule-based formalism, in which rules take the form pattern → value, where "pattern" is a Boolean condition over agents, and "value" is a numeric value. Ieong and Shoham showed that, for a class of what we will call "basic" MC-nets, where patterns are constrained to be a conjunction of literals, marginal contribution nets permit the easy computation of solution concepts such as the Shapley value. However, there are very natural classes of coalitional game that require an exponential number of such basic MC-net rules. We present read-once MC-nets, a new class of MC-nets that is provably more compact than basic MC-nets, while retaining the attractive computational properties of basic MC-nets. We show how the techniques we develop for read-once MC-nets can be applied to other domains, in particular, computing solution concepts in network flow games on series-parallel networks.