Have You Played... Shadow President?
Commander in pants
One of several things I lamented during the golden age of abandonware (an era with a contested definition, but generally "the 2000s"), was a dearth of games explicitly about politics. Simulators in particular were practically unheard of, which is how I ended up playing 1993's Shadow President, a game about getting frustrated and trying to invade the United Kingdom.
You have near absolute power as the President, which sounded unlikely to me once. You view the world through a satisfyingly chunky strategic interface, clicking on any country at any time for a report on its background, its economy, its relationship with the US, its strategic significance (the game's heaving with information from the CIA world factbook, which is probably even more interesting today for its obsolescence), and so on. You also use this interface to enact decisions. Some are long-term, like the adjustment of various forms of aid, while others are one-off gambles aimed at either weakening troublesome nations, improving relations through cultural exchanges and the like, or simply boosting your popularity back home.
The standard game starts immediately before the first Gulf War, which is, politically speaking, a pain in the arse. In theory you're meant to use your enormous influence to defuse the situation somehow, or put a decisive, stable end to the war with as little fallout (figuratively... hopefully) as possible. You can do this by committing military forces, by putting economic pressure on troublemakers, by isolating enemies, or perhaps by extending an olive branch that might backfire horribly.
What you will actually do, of course, is cut off all military and espionage aid to Israel, fund health and education programmes across the world, then get pissed off when everyone reacts with anger, and launch two thousand nuclear missiles at Britain, the condescending imperialist bastards. The entire world then retaliates against your innocent populace while you cackle insanely in your bunker, scoffing porridge in your kecks while pressing random buttons until all your advisors resign and you're either impeached, or a spray of gunfire demolishes your screen and brain. A land should have kings, that it can behead them.
There are many reasons why I am not the President of the United States.