The grand surplus value and repeated cooperative cross-games with coalitional collaboration

We propose a value for games with transferable utility, called the grand surplus value. This new value is an alternative to the Shapley value, in particular in games where, in the process of coalition formation, two overlapping coalitions can, at least hypothetically, guarantee their members their full worth simultaneously. Central is the concept of the grand surplus, which is the surplus that results when all coalitions, each lacking one player of the player set, no longer act individually but only cooperate as the grand coalition. All the axiomatizations presented have an analogous equivalent for the Shapley value, including the classics by Shapley and Young. Especially for a new class of games, called repeated cooperative cross-games with coalitional collaboration, the grand surplus value seems preferable to the Shapley value. A new concept, called multiple dividends, provides a close connection to the Shapley value.