In the House Rules section of this forum, a few ideas have sometimes been kicked around for rules that would allow a free-for-all, Risk-style, global domination A&A game. But under the official rules of A&A, the Allies and the Axis play as teams against each other. The Allied nations don’t fight each other and the Axis nations don’t fight each other. At most, in some of the games, there are initial phases in which some of the player nations are neutral.
A&A is like a massive version of Risk only in the sense that both games use a similar basic four-stroke engine: units fight battles, battles win territory, territory generates income, and income buys units.