A slight nitpick: I wouldn't describe politics as anything remotely near zero-sum. The actions of the players of a country's game of politics have very far-reaching effects on the citizens and residents of that country, and in some cases of the residents of the entire world.

The actions of the players definitely do affect the world at large in ways outside the scope of the game, which makes it about as far from zero-sum as it could possibly be. I'm pretty sure that this changes the outcome of your thought experiment dramatically.