Hamiltonian potential functions for differential games

We introduce the concept of Hamiltonian potential function for noncooperative open-loop differential games and characterise necessary and sufficient conditions for its existence. We also identify a class of games admitting a Hamiltonian potential and illustrate appropriate examples pertaining to oligopoly games where price or quantity competition goes along with noncooperative investments either in advertising or in R&D, so as to provide a plausible intuitive interpretation of the meaning of the Hamiltonian potential.