A Formal Theory of Cooperative TU-Games

Authors:
Marc Daumas;Érik Martin-Dorel;Annick Truffert;Michel Ventou
Affiliations:
ELIAUS (EA 3679 UPVD), Université de Perpignan, Perpignan, France 66860;ELIAUS (EA 3679 UPVD), Université de Perpignan, Perpignan, France 66860 and LAMPS (EA 4217 UPVD), Université de Perpignan, Perpignan, France 66860;LAMPS (EA 4217 UPVD), Université de Perpignan, Perpignan, France 66860;LAMPS (EA 4217 UPVD), Université de Perpignan, Perpignan, France 66860
Venue:
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Year:
2009

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Abstract

Results of game theory are often the keys to decisions of economical and political executives. They are also used to create internal tools of many decision making software. For example, coordination games may be cooperative games, when the players choose the strategies by a consensus decision making process, and game trees are used to represent some key cooperative games. Our theory of cooperative games with transferable utilities makes it possible to deliver a formal certificate that contains statements and proofs with each result of any procedure in theory of cooperative TU-games. Such formal certificates can be archived and audited by independent experts to guarantee that the process that lead to the decision is sound and pertaining. As we use an automated proof checker, the review only has to guarantee that the statements of the certificate are correct. The proofs contained in the certificate are guaranteed automatically by the proof checker and our formal theory.