Is it possible for the same job company to have different minimum wage pay? For example, sports authority in one area may have different minimum wage than another.

What I can tell you is in different states the wage can be different  an example would be in Kentucky (where I live) fast food jobs start at our (newly raised) minimum wage of $7.65.  I have a nephew who lives in NYC where they pay fast food to start around 12.00 to 14.00 to start