It doesn't matter how many people are mining, coins are generated at a fixed rate. The difficulty to mine coins is varied automatically to assure this.

It's this difficulty that affects miners when more folks start mining. In effect they are taking the known portion of the pie (coins to be mined in a given time frame) and slicing it into many more pieces. This means that you have to work for a much longer time to have a nice large piece of pie with plenty of room for ice cream and whipped cream on top.