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I read this in an anthology in the late '80s/early '90s, Asimov is stuck in my mind as either the author or editor, although that may be totally incorrect.
What I can remember is there was a glass Coke bottle (I think this was revealed at the end), and it was very valuable as it was the last one.
Possibly it was told from the thief's point of view.
Are you sure you're not thinking of the 1980 movie The Gods Must Be Crazy? The plot is kicked off by a Coke bottle found by a Sho tribe and the chaos it brings.
Xi and his San tribe are "living well off the land" in the Kalahari Desert. They are happy because of their belief that the gods have provided plenty of everything, and no one among them has any wants. One day, a Coca-Cola bottle is thrown out of an airplane and falls to Earth unbroken. Initially, Xi's people suppose this strange artifact is another "present" from the gods and find many uses for it. (They employ it as a crafts tool, blow the top to make music, etc.) But unlike anything that they have had before, there is only one glass bottle to go around. With everyone wanting it at once, they soon find themselves experiencing envy, anger, and even violence.
"The Transall Saga" comes to mind. The Coke bottle, or some piece of it, clues the protagonist/reader in on the fact that
He's on future Earth.
It's a bit outside of your listed timeframe, but it hits these points:
You may be thinking of "Game Preserve", a short story by Rog Phillips (pseudonym of Roger Phillips Graham), first published in If, October 1957, and available at the Internet Archive (click here for download options). It has been reprinted under a number of covers; you may have read it in the 1989 anthology The Great SF Stories #19 (1957) edited by Isaac Asimov and Martin H. Greenberg.
What I can remember is there was a glass Coke bottle (I think this was revealed at the end),
Indeed, it is referred to throughout the story as an "It", and only at the very end do we find out what it is:
Sobs welled up within him, spilled out, shaking his small naked body. He cried as he hadn't cried since he was a baby.
And the empty Coca Cola bottle, clutched forgotten in his hand, glistened with the rays of the setting sun . . .
and it was very valuable as it was the last one.
I don't think it was the last one. Here's the scene where the boy finds it:
Elf leaped to his feet, paused to stretch elaborately, then splashed into the stream. As soon as he caught a fish he climbed out onto the bank and ate it. Then he turned to his search for a little It. There were many lying around, all exactly alike. He studied several, not touching some, touching and even nudging others. Since they all looked alike it was more a matter of feel than any real difference that he looked for. One and only one seemed to be the It. Elf returned his attention to it several times.
Finally he picked it up and carried it over to the big It, and hid it underneath. Big One, with shouts of sheer exuberance, climbed up onto the bank dripping water. He grinned at Elf.
