Yes, they can make you work for the competition: your employer decides who you work for, what your work is, what your duties, are, etc. Your employer can have you do any work for anyone they want.No, they can't make you work without being paid for your time, if you are an hourly employee: hourly employees must be paid (including overtime, as applicable) for all work done at their employer's instructions or request. However, if you are salaried, you salary covers all work you do; they do not need to provide additional compensation.