Weighted Myerson value for Network games

TL;DR

This work introduces the weighted Myerson value for Network games, extending the classical Myerson value by incorporating player weights that reflect differing abilities to form links. It provides two axiomatic characterizations—one via Component Balance and Weighted Bargaining Power, the other via Efficiency, Network Specific Player Anonymity, Superfluous Link Property, and Additivity—and connects the value to a weighted network potential. To bridge theory and application, the authors present two non-cooperative bidding mechanisms that implement the weighted Myerson value as SPNE outcomes, with Mechanism II showing convergence to the same allocation in the bargaining limit as $\rho\to1$. The approach generalizes existing concepts (weighted Shapley and graph-restricted games) and suggests extensions to more complex network structures such as multigraphs or hypergraphs, offering a principled method for fair value allocation in heterogeneous networks.

Abstract

We study the weighted Myerson value for Network games extending a similar concept for communication situations. Network games, unlike communication situations, treat direct and indirect links among players differently and distinguish their effects in both worth generation and allocation processes. The weighted Myerson value is an allocation rule for Network games that generalizes the Myerson value of Network games. Here, the players are assumed to have some weights measuring their capacity to form links with other players. Two characterization of the weighted Myerson value are provided. Finally, we propose a bidding mechanism to show that the weighted Myerson value is a subgame-perfect Nash equilibrium under a non-cooperative framework.

Theorems & Definitions (18)

• Example 1
• Example 2
• Theorem 1: Jackson2005, page 134, Theorem 1
• Theorem 2: belau3, page 80, Theorem 2
• Lemma 2
• proof
• Definition 5
• Theorem 6
• proof
• Theorem 7