"Generalized Shapley axioms and value allocation in cooperative games via Hodge theory on graphs"
Abstract: Lloyd S. Shapley introduced a set of axioms in 1953, now called the Shapley axioms, and showed that the axioms characterize a natural allocation among the players who are in grand coalition of a cooperative game. Recently, A. Stern and A. Tettenhorst showed that a cooperative game can be decomposed into a sum of component games, one for each player, whose value at the grand coalition coincides with the Shapley value. The component games are defined by the solutions to the naturally defined system of least squares - or Poisson - equations via the framework of the Hodge decomposition on the hypercube graph.
Hosts: Ari Stern and Jonathan Weinstein (Economics)