I'm not sure, but it looks like a moen m core series 2 cartridge valve style. If it's a moen, pf or delta give them a call and they will send you out a new cartridge for free. Thermostatic temperature control/balanced = expensive cartridge. Your call.
I know delta has 1222 and 1225 style cartridge which doesn't match what you have at all. The moen m core series 2 looks close to what you have. Both moen and delta use that same style trim package you have. But usually it says either moen or delta right at the bottom of the trim and I don't see it in your photos, so I'm not sure.