Retailers all have the right to discount your book if they choose. You can rest assured a retailer's discount for your print edition book will not cut into your proceeds. When a retailer discounts a book, they are the ones eating the cost of the price reduction. In other words, your earnings will still be based on the original retail price.

The one exception to this is if Amazon decide to discount your eBook in order to match a lower price it finds elsewhere. In this case, your eBook earnings will be based on the discounted price.