Learning to identify winning coalitions in the PAC model

Authors:
Ariel D. Procaccia;Jeffrey S. Rosenschein
Affiliations:
The Hebrew University of Jerusalem, Jerusalem, Israel;The Hebrew University of Jerusalem, Jerusalem, Israel
Venue:
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Year:
2006

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Abstract

We consider PAC learning of simple cooperative games, in which the coalitions are partitioned into "winning" and "losing" coalitions. We analyze the complexity of learning a suitable concept class via its Vapnik-Chervonenkis (VC) dimension, and provide an algorithm that learns this class. Furthermore, we study constrained simple games; we demonstrate that the VC dimension can be dramatically reduced when one allows only a single minimum winning coalition (even more so when this coalition has cardinality 1), whereas other interesting constraints do not significantly lower the dimension.