For some of that, there's some old and quite solid math -- differential game theory. See, say, Rufus Isaacs, long a professor at Johns Hopkins and who IIRC did

For some of that, there's some old and quite solid math -- differential game theory. See, say, Rufus Isaacs, long a professor at Johns Hopkins and who IIRC did his first work at a US Navy lab and see also Avner Friedman.