I can tell you with confidence that dogs can tell if you are treating them fairly. They know through visual awareness if you gave another dog one extra treat. They know through olfactory awareness if you gave another dog different toppers on their food. They know if you toss the toy to the other dog more often. They can certainly hear the sound of your pitch when you offer the other dog more excited affection. They also know when they enter your sitting room, who most often gets the spot closest to you.
I broke the rules
I want to tell you about an example, when I was called out by Jade for not being fair with toys! While playing fetch with her at about six months of age, Drake became interested in her new red squeaky ball. I should have just let him smell it, however, I threw it close to him so he could beat her to it. I knew he wanted to check it out, and being lazy, I just tossed it instead of walking over to him. That was wrong of me! Jade snatched it from his mouth and trotted about 20 feet away from me and spit it out.
Jade’s behavior changed
This was out of character for her, as she always drops it at my feet. Puzzled, I looked at her. My six month old puppy looked me in the eye, looked at Drake, looked at her ball on the ground, and then stared at me. I tried not to laugh. She was totally right, as I have been trying to get them to play with different toys, to prevent them from stealing each others. 
I broke the rules! I should have walked over and just let Drake smell her new toy, not tossed it to him.
My apology
I knelt down, coaxed her to me, and promised to be more fair. I told Drake to get his soccer ball and we continued playing, Drake with his orange soccer ball and Jade with her red squeaky toy. Everyone’s needs were met that day, thanks to Jade. Her social confidence and understanding of the rules of the games we play allowed her to inform me that I was not playing fair. Judy will be consistently following her own rules! 
with different toys.