Price control is illegal.
The retailer is supposed to be able to decide upon their own profit level.
A wonderful theory that never happens in real life.
In theory the big box stores pay Cub the same price as the corned dealer.
In practice that never happens either.
At the beginning of a season everyone charges as much as they can because demand is high.
Latter on as demand drops so do prices.
Corner shops get x number of days to pay Cub for the mower so when X is getting close they will discount that particular mower ( but not the identical one next to it ).
Big box get y number of days after the mower is sold to pay Cub for it.
While "price fixing" may be illegal, there is no law that prohibits a manufacturer from entering into legal binding contracts with retailers/dealers that dictate the selling price of a product and that those prices are subject to change based on Manufacturer promotions and negotiated sales.
To answer your question, you will not likely find an XT1 mower cheaper at one store than another unless that store is offering a special sale that they have been allowed to have. When Cub Cadet advertises their national promotions, the prices will usually change everywhere the affected models are sold. Profit margins are small on less expensive mowers, so if negotiations can be had, there is likely little wiggle room. I don't see many people haggling on price of a sub $3k mower.