The Lovebirds Problem: Why Solve Hamilton-Jacobi-Bellman Equations Matters in Love Affairs

摘要

The lovebirds problem consists in finding the compromise between well-being and efforts that are necessary to sustain a sentimental relationship. According to a modeling introduced by J.-M. Rey, the problem can be described as finding the initial data for a certain dynamical system, guaranteeing that the associated trajectory belongs to the stable manifold. We further discuss this interpretation by means of the Dynamical Programming Principle and the Hamilton-Jacobi-Bellman framework. It allows us to propose an algorithm that determines numerically the solution of the lovebirds problem.