The standard notion of rationality used in game theory is maximizing expected payoff given some subjective belief (a probability distribution) over what the other players do. Let's also assume everyone cares only about winning.
So what is the largest number a rational player could play in this game? If everyone else plays $99$, one could win by playing $98$. If you think they play something smaller, you would want to play an even smaller number. So a rational player will never play $99$. Now, if you are sure everyone else is rational, you know that nobody else will play $99$ and for the same reason as before, $98$ is not a best response to any behavior compatible with the assumption that everyone is rational. Now if you think that everyone thinks that everyone is rational, you can rule out $97$. Continuing this way, you can rule out everyone playing anything but $0$ and this is the only outcome compatible with common knowledge of rationality.
Note that the assumption that everyone knows that everyone knows that... everyone is rational is more and more demanding and probably unrealistic, the longer the chain of reasoning goes. So there is very little one can actually say about how to play the game.
Something that does help a bit is weak dominance. Even though playing $98$ is compatible with rationality, note that whenever $98$ wins, $97$ would win too and there are imaginable cases (with many players) where $97$ wins but $98$ does not. by a similar argument, you might not want to play anything larger than $66$.