Decomposition of Network Communication Games

Bas Dietzenbacher,Ruud Hendrickx,Peter Borm

doi:10.2139/ssrn.2701736

Abstract

Using network control structures this paper introduces network communication games as a generalization of vertex games and edge games corresponding to communication situations and studies their decomposition into unanimity games. We obtain a relation between the dividends of the network communication game and the underlying transferable utility game, which depends on the structure of the undirected graph. This relation extends the computational results for tree communication networks to general undirected graphs and is used to derive new characterizations of the Myerson value and the position value. Moreover, network communication games also allow to consider both the vertices and the edges of the graph as players, leading to a new network value.

Highlights

Cooperative game theory analyzes allocations of joint revenues among cooperating players, taking the economic possibilities of subcoalitions into account
This paper introduces a general class of network communication games and a corresponding class of network control values for communication situations
We conclude this paper with two examples of possible extensions of the decomposition theory to more general communication networks: undirected multigraphs and hypergraphs

Summary

Introduction

Cooperative game theory analyzes allocations of joint revenues among cooperating players, taking the economic possibilities of subcoalitions into account. Myerson (1977) introduced the graph-restricted game corresponding to a communication situation in which each coalition of vertices is assigned the sum of the worths of the components in its induced subgraph. We refer to this game as the corresponding vertex game. We obtain a relation between the dividends in the network communication game and the underlying transferable utility game, which depends on the structure of the communication network This relation is used to extend the results of Owen (1986) and Borm et al (1992) for cycle-free networks to all undirected graphs.

Preliminaries

Network control values

Concluding remarks