On the numerical solution of a free end-time homicidal chauffeur game

Abstract

A functional formulation of the classical homicidal chauffeur Nash game is presented and a numerical framework for its solution is discussed. This methodology combines a Hamiltonian based scheme with proximal penalty to determine the time horizon where the game takes place with a Lagrangian optimal control approach and relaxation to solve the Nash game at a fixed end-time.

Game Theory Methods for Pursuit-Evasion Problems

“…Pursuit-evasion game is an effective mathematical modeling approach to solving pursuit-evasion problems. The most commonly seen pursuit-evasion games are multi-player pursuit-evasion games, such as cops and robber games [1] , homicidal chauffeur games [2] , etc. Sometimes the pursuer needs to have the ability to ensure the capture of all the evaders.…”