I'm attempting to research competitive games of a specific type, where the players aren't ever in "direct" competition with each other, and having difficulty describing them. General examples include racing games, where players individually try to get the best time on a track, classic arcade games, where players attempt to obtain the highest score, or, for a more recent example, the "daily challenge" announced recently for the PC version of Spelunky, found here: http://spelunkyworld.com/dailychallenge/
The key aspect is that (for lack of a better word) the games are completely asynchronous: Player A's playthrough never has a direct effect on Player B, and vice-versa. "Asynchronous" isn't a good enough term, though, because certain turn-based board and strategy games (such as Scrabble and Chess) can be played asynchronously, but they don't fit the criteria: they are directly competitive in that Player A's turn directly affects how Player B will respond or play. In the types of games that fit the word I'm looking for, a player's performance is unaffected by all and any of the other players competing.
Is there a word or phrase to describe this type of competition?