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Reasoning about coalitional games

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Non-Transferable Utility (NTU) games are one of the fundamental models in cooperative game theory, and have been widely used in multi-agent systems research over the past decade. This work is the first to develop formal (logic-based) knowledge representation languages for NTU games. The paper thoroughly investigates two logics for reasoning about cooperative games, which demonstrate the “bare minimum” logical apparatus required to reason about such games, investigates the complexity of these logics, and develops reasoning algorithms for them. The results are presented via formal proofs, and the work illustrates how the formalism can be used in practice.

This 34-page journal paper includes material from a preliminary 8-page conference paper entitled “On the Logic of Coalitional Games“, by the same authors presented at AAMAS-2006 conference (sections 3-1–3.3 of the journal paper). The submitted paper extends this work hugely, giving completeness results and a decision procedure for the logic presented in the conference version, proving a number of game theoretic results within the logic, and in addition presenting a totally new logic for coalitional games. None of this previous work was submitted to RAE2008.