A Formal Theory of Cooperative TU-Games

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.