Journal of Economic Education
The need to understand surplus-sharing rules in cooperative game theory occurs at both the undergraduate and graduate levels. The rules are generally depicted as mathematical problems that entail the calculation of a vector of allocations. This Web page provides a downloadable program that enables users to interactively generate geometrical depictions of the rules for an unlimited number of three-player games. The program (1) demonstrates graphically how the simplex (i.e., area of potential cooperation) is shrunk to its corresponding core on the basis of the game’s characteristic function (i.e., the specification of the payoffs for each of the seven possible coalitions, including the grand coalition of all three players), (2) calculates the Shapley value, nucleolus, and per-capita nucleolus surplus-sharing allocations for the game, and (3) depicts graphically the locations of these allocations in the corresponding cores. The program provides game theory practitioners with a tool to visualize the important elements and outcomes associated with cooperative games.
Caplan, Arthur J., and Yuya Sasaki. "Interactive Geometry for Surplus Sharing in Cooperative Games." Journal of Economic Education, 37(3), 382