Tools for Calculating Allocations in Game Theory using Exact and Approximated Methods
Banzhaf Index (approximated)
Banzhaf Index (exact)
Banzhaf-Owen Value
Banzhaf-Owen Value
Banzhaf-Owen value
Banzhaf value
Centroid of the core of the game
coalitions
Approximated core of the game
Exact core of the game
Vertices of the core of the game
Egalitarian value with a priori unions
Egalitarian value
Equal Surplus Division value with a priori unions
Equal Surplus Division value
Myerson value with a priori unions
Myerson value
Owen value (approximation)
Owen value (exact)
Owen value
Predecessor
Shapley value (approximation)
Shapley value (exact)
Shapley value
The main objective of cooperative Transferable-Utility games (TU-games) is to allocate a good among the agents involved. The package implements major solution concepts including the Shapley value, Banzhaf value, and egalitarian rules, alongside their extensions for structured games: the Owen value and Banzhaf-Owen value for games with a priori unions, and the Myerson value for communication games on networks. To address the inherent exponential computational complexity of exact evaluation, the package offers both exact algorithms and linear approximation methods based on sampling, enabling the analysis of large-scale games. Additionally, it supports core set-based solutions, allowing computation of the vertices and the centroid of the core.
Useful links