The Power Allocation Game on A Network: Balanced Equilibrium

TL;DR

This paper introduces and analyzes the concept of balanced equilibrium in a power allocation game among countries, establishing conditions for its existence and linking it to classical graph problems.

Contribution

It defines the balanced equilibrium in the context of international power games and connects its existence to graph-theoretic problems like maximum matching and max flow.

Findings

Conditions for equilibrium existence in various network structures

Link between balanced equilibrium and Hall's Maximum Matching

Connection to Max Flow problem in networked environments

Abstract

This paper studies a special kind of equilibrium termed as "balanced equilibrium" which arises in the power allocation game defined in \cite{allocation}. In equilibrium, each country in antagonism has to use all of its own power to counteract received threats, and the "threats" made to each adversary just balance out the threats received from that adversary. This paper establishes conditions on different types of networked international environments in order for this equilibrium to exist. The paper also links the existence of this type of equilibrium on structurally balanced graphs to the Hall's Maximum Matching problem and the Max Flow problem.