The Power Allocation Game on A Network: Computation Issue

TL;DR

This paper introduces two algorithms for computing the equilibrium set in a network power allocation game, with one providing geometric insights and the other enabling efficient simulation-based predictions, demonstrated through a real-world case study.

Contribution

It presents a geometric characterization of the equilibrium set and a simulation algorithm for efficient computation, applied to a geopolitical conflict scenario.

Findings

The equilibrium set forms a collection of convex polytopes.

The simulation algorithm efficiently generates the equilibrium set.

Application to a North Korea crisis case study demonstrates practical relevance.

Abstract

In this paper two algorithms with the goal of generating the equilibrium set of the power allocation game first developed in \cite{allocation} are proposed. Based on the first algorithm, the geometric property of the pure strategy Nash equilibrium set will be proven to be a collection of convex polytopes. The second, simulation-based, algorithm is developed to overcome the shortcoming of the first algorithm in terms of generating the equilibrium set efficiently and then making policy-relevant predictions based on the set. The second algorithm will be usefully applied to a real-world case study, which draws on the current crisis between North Korea and certain key players including the US and China.