Game of Power Allocation on Networks: Balancing Equilibrium

This paper defines and studies a special kind of equilibrium termed as “balancing equilibrium” which arises in the power allocation game in [14]. The equilibrium has both unique mathematical property and realistic implications. In the equilibrium, all countries in antagonism have to use all of their own power to counteract the received threats, and the threat made to each adversary only equalizes the threat received from that adversary. This paper establishes necessary and sufficient conditions for countries’ power in order for this equilibrium to exist in different types of networked international environments. It also links the existence of this equilibrium in PAGs on structurally balanced graphs to the Hall’s Maximum Matching problem and the Max Flow problem.