See this definition from Wikipedia.
In modern psychology, Machiavellianism is one of the dark triad personalities, characterized by a duplicitous interpersonal style, a cynical disregard for morality and a focus on self-interest and personal gain.
Change the personal to the national and you have a Putin leadership style, which Trump admires.
So let's say, for shits and giggles, that newly elected President Donald Trump was ruled by self-interest, not only his own and his ego's, but the country's self-interest without regard to current and historical US "Morality".
What would that look like? In many ways, it might look a lot like Orwell's A Brave New World, in which the world was divided up into sphere's of control. Only in the book, it was America, Russia and Europe - now it would more likely be America, Russia and China.
A related, but perhaps more realistic, example would be a multipolar "great power" world like Europe in the 1800s and early 1900s. With different major powers being played off against each other. In this scenario, we would give Russia a free hand in it's near abroad (like Ukraine), we would get a free hand in our near abroad (like Central America), and we would effectively give Chinese control of SouthEast Asia (and the 9 dash line). In this way a bit like A Brave New World.
But there would be plenty of independent players. European powers (and a few others, like Brazil, South Africa, India, Australia) would remain independent and free to play one power off another (as Poland, Belgium and Serbia did in the olden days), trying to buy time.
And then, of course, Nuclear weapons would allow a country to punch above its weight. It may not make them powerful enough for a sphere of influence, but would give them some safety against attacks.
Expect a lot more nuclear weapon states pretty quickly. You can bet your ass Ukraine regrets giving up their nucs for the (treaty guaranteed) promise of border integrity now! North Korea proves that nucs provide safety as long as you don't attack anyone else (threaten all you want). Countries that can get them quickly, would (Japan, South Korea, Australia, Brazil, Argentina, Saudi Arabia, Iran - well most of the Middle East in general).
For most of the world it is a pretty bad deal. If the US doesn't at least pay lip service and occasional support for democracy and capitalism, then there are no norms to ignore. With more nucs, the only option against the current powers would be terrorism that is stateless and harder to defend against.
For the US public, it may actually be better in the short term. We could reduce our defense expenses (we could spend 1/2 of what we do now and still be head an shoulders the most powerful of the great powers), lower our global footprint and forget about places that don't matter to us (Afghanistan, Yemen, Somalia). It might also reduce terror against Americans (if we allow the terrorist to declare victory abroad - a tough thing for a President to swallow).
Where the good news breaks down is with the US (and other) multinational corporations and all the world's consumers. The world economy, including the US economy, has made amazing strides by the current US led multinational consensus (as defined by the Western Powers). People have risen from poverty (1 BILLION people over the last decade) and become richer and safer. If you upend that consensus, no one is sure what else gets upended.
The Western consensus has, with various tweaking, provided a nice basis for world economic growth and more personal wealth and freedom (relative to historical levels). How much of that is now fixed and how much could be rolled back? Tariffs and national barriers might easily pop up again, making everyone poorer. That is where the questions (and instability) lay.
Without the Western Consensus, what are people willing to give up?
The United States public has proven that we are willing to give up plenty of freedoms and privacy for safety. The new President's voters are willing to give up healthcare and long term social norms for anger. The Chinese public has proven that they are willing to give up plenty of freedom and political participation for wealth. The Russian public has proven they are willing to give up plenty of wealth for ideology (arguably the English public, the same).
It is, I think, a recipe for long term disaster. It turns the world economy into a win/lose scenario (in theory if not in fact) and resentment would run high very quickly. Powers that see the world as a zero sum game will go to war when their odds look good.
The Western Consensus is that the economy, health, welfare and liberty are not zero sum games and can be win/win for all involved. If President Trump is able to convince Americans this isn't true, then watch out. Americans (like anyone else) hate being played as suckers.