What are some strategies for this number game?

I just recently read about this number game, and I am interested in what sort of strategies might exist. I have simplified the game slightly.

There are five players. Each round, all of the players choose a number 1–10 without knowing the choices of the other players. Then, each player’s guess is revealed, and the winner is the person with the lowest number that no other player chose. The winner of the round gets one point. The winner of the game is the person with the most points after any given number of rounds.

What are some strategies that could be used to increase the odds of winning this game?