Now the beast which I saw was like a leopard, his feet were like the feet of a bear, and his mouth like the mouth of a lion. The dragon gave him his power, his throne, and great authority. Revelation 13:2
From my understanding, it will extend to all nations of the world. These are my reasons for holding to this view.
The beast will be the agent of satan, who is the god of this world. Notice from the passage above that satan does not only give his power and authority to the beast, but also his throne. That the god of this world has a throne implies that he has a kingdom, and let's understand that the governments of the nations of the world are proxies to this satanic kingdom, therefore, it will not be difficult for him, the devil, to bring all nations under his subjection. Actually, they are already his subjects by reason of their rejection of the lordship of Jesus Christ.
The throne of the dragon, given to the beast, is not a territorial authority, it is global, because it is the throne of the god of this world. At that time, the entire world will be under the sway of satan. "So they worshiped the dragon who gave authority to the beast; and they worshiped the beast, saying, “Who is like the beast? Who is able to make war with him?” Revelation 13:4. Satan's kingdom, ruled by the beast, will be a literal world government.
"And I saw three unclean spirits like frogs coming out of the mouth of the dragon, out of the mouth of the beast, and out of the mouth of the false prophet. For they are spirits of demons, performing signs, which go out to the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty." Revelation 16:13-14. By these demon spirits, the dragon and the beast are able to enlist the rest of the world to be part of their global project.
Before the event of Revolution 17:12-13 takes place, the nations of the earth will already be in the control of the dragon and the beast, therefore, getting them to submit to a global ruler, which will happen in Revelation 17, will not be a difficult task. There will be only one nation in the world at this time that will resist this arrangement, Israel, and she will pay severely for it. The equation will, however, change when Jesus Christ comes riding on the white horse with His hosts, and, then, the kingdoms of this world will become the kingdoms of our Lord and Christ fulfilling Daniel 2:44 "And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand forever." Hallelujah to the Lord whose name is the Word of God, the King of kings and Lord of lords.
What I have presented is a brief overview of what is most certain to happen in the last days of this age, according to the bible.
Toni