TITLE:
Graph Games with Component-Based Control Structures
AUTHORS:
Letian Chen, Guang Zhang
KEYWORDS:
Cooperative Game, Graph Structure, Component Restriction, Allocation Rule
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
20,
2025
ABSTRACT: This paper investigates allocation rules in graph-structured cooperative games (hereinafter referred to as graph games) by integrating the notion of network control. A component-restricted game and the component control value are proposed through treating each connected component as a virtual player (termed a component player), under the stipulation that only coalitions attended by component players are eligible to obtain coalitional worth. The component control value initially assigns a Shapley payoff (Shapley value, SV) to every player, and the SV of each component player is subsequently redistributed equally among all original players belonging to its corresponding connected component. Thereby, an axiomatic characterization of this allocation rule is established, demonstrating that the component control value constitutes the unique solution satisfying component efficiency and component-restricted fairness in graph games.