Here's what I remember of the plot:
Russia and the US both build a supercomputer that's designed to play chess. They meet in a highly publicized event where the two computers will play each other.
They flip to see who goes first, and the US wins. Everyone watches with bated breath as the US computer makes its first move. And then it's Russia's first turn, and the computer... concedes.
The implication is that the Russian computer solved all possible moves, and quit because it realized it couldn't win going second if the US computer played perfectly.
I believe this was in a short story, probably in some sort of anthology book. I read it 10-15 years ago, and it could be much older than that - it had a very "cold war" feel. It was in English.