ELi5: How do Co-operatives work?

Question

There are dominant supermarket players in my country under the same Parent and these supermarkets operate in a Co-operative structure (Not franchise) where the Parent essentially acts like a support centre for the stores. Under this structure, does it not mean that the parent has no say in prices of grocery and instead it’s the members (aka owners of the grocery stores) that have the say in prices of grocery? I know the head office of the Parent works with suppliers to determine costs of items for the supermarkets and understand could squeeze suppliers dry from that which would get them negative media attention. But am I correct to believe in a co-operative the Parent company doesn’t get to set prices for the members? Whenever there is negative media attention on high grocery prices it’s always directed towards the Parent rather than the supermarkets themselves and can’t get my head around why

In: Economics