Efficiency Axioms for simplicial complexes
arXiv:2001.00779
Abstract
We study the notion of efficiency for cooperative games on simplicial complexes. In such games, the grand coalition may be forbidden, and, thus, it is a non-trivial problem to study the total number of payoff of a cooperative game . We address this question in the more general setting, by characterizing the individual values that satisfy the general efficient requirement for a generic efficiency assignment. The traditional and the probabilistic efficiency are treated as a special case of this general efficiency. Finally, we introduce a new notion of efficiency arising from the combinatorial and topological property of the simplicial complex . The efficiency in this scenario is called simplicial and we characterize the individual values fulfilling this constraint.
12 pages, 1 figure