Here our list of predators is short, Cats and dogs, hawks (out in the country this is a problem) stoats( also in the country) and hedgehogs, which are my main problem. Because of this the houses to my coops are all hedgehog proof and are closed off at night, especially because of the chicks who don't stand a chance. Most people don't realise or believe that hedgehogs do so much damage but they do and its problematic, they steal eggs, chicks and full sized birds by eating them from the inside out. Rats are also a problem but once again only in the country/ near water. I live on the edge of the city so I don't have the problem of rats, stoats or hawks, and my dog keeps all other dogs and cats especially away ( both of us hate cats) . egg thieving can start out as just that and esculate when there is no eggs left and they will go for the birds, It would be rats, stoats, weasels, hedgehogs, ferrits, foxes, snakes ive also heard badgers will steal eggs. If I was you I would look into it/ set up traps and make sure everything is predator proof, loosing birds is awful, especially when they are pets or they went slowly and in an agonizing way . If its taking Dummy eggs then its hungry, finding out what it is, is a must.
I don't set out dummy eggs I just have a large bucket of water, a club/ mag light torch and go out each night and check everything over, do a basic countup of the older birds, put the younger idiots that sit outside away and hope for the best.