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Games on ordered structures : recent advances

Among the recent advances in cooperative game theory, a notable fact is the emergence of new notions of games which are defined on more general structures than the usual Boolean lattice of the subsets of the universal set. Apart of the mathematical interest brought by such works, the main motivation lies in an attempt to model the real world in a more accurate way. The main difficulty is to find the right definitions for the usual tools and concepts used in the theory: these are essentially solution concepts like the Shapley value and the core, but our discussion will also include the Choquet integral and the entropy, which are more on the side of decision theory. Our aim is to provide a survey of recent advances along these lines. In all our discussion, we consider the set of players to be finite. We denote it by N , and |N | = n.