You don't want to shift AT peak power, you want to shift at the point that the torque figure from the next gear starts to better the torque figure you are currently putting to the road.
Doing that means you generally find yourself operating in an area surrounding peak power, so if peak was at 6000rpm, you would be shifting at say 6500rpm which would leave you at 5500rpm after the shift.
Maintaining the most amount of torque you can put to the road is the aim, shifting at peak power is often too soon and means you shift up into a lower torque figure and your acceleration is slower.
It depends entirely on the engine and gearing (the optimum point for each gear change will be different as the difference in ratios changes) and is something that's really way too in depth for a kid playing a game