In geopolitics, this is the greatest show on earth. For the best part of a week, the world's leaders – more than 150 of them – will mingle, bargain and argue over the state of the world at the UN general assembly in New York.

For much of the proceedings, "show" is the operative word. When the presidents and prime ministers mount the green marble podium, there will be a strong element of theatre. They will be playing to different galleries, declaiming their positions to their peers in the chamber, but also to domestic audiences.

The drama will be greater than ever this year, at the 70th session of the UN general assembly, known inside the institution by its acronym Unga (rhyming with hunger). Within the space of two hours on Monday morning, Presidents Barack Obama, Xi Jinping, Vladimir Putin, Hassan Rouhani and François Hollande will take their turn to speak. Each will try to anticipate and respond to the other, seeking rhetorical advantage and one-upmanship in their claims to global leadership. The global balance of power will be laid out in the open.