Senior Honors Thesis & Final ARTU Presentation: "Hodge Decomposition and the Shapley Value of a Cooperative Game"

Alexander Tettenhorst

Abstract: In 1953, Lloyd Shapley introduced the Shapley Value, a solution concept for a cooperative game that assigns a unique feasible payoff profile based upon the expected marginal contribution made by each player to the grand coalition. Using methods from linear algebra and Hodge Theory, in this paper we develop a new approach to finding the Shapley Value for any cooperative game, which proves to be more efficient than the method originally outlined by Shapley.

Advisor: Ari Stern