TITLE:
A Value for Games Defined on Graphs
AUTHORS:
Néstor Bravo
KEYWORDS:
Graph Theory, Values for Graphs, Cooperation Games, Potential Function
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.5,
May
14,
2024
ABSTRACT: Given a graph
g=(
V,A
)
, we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.