But, also, if they waited the farmer might take the crop. From the point of view of the bird, not-quite-ripe fruit is nearly as good, nutrition-wise. So, not really a "tragedy".
Nope. They're dropping the green fruit on the ground, and never go back to it. They're nearly destroying their own food supply, in an effort to beat the rest of the flock to that one berry that ripens early.
I'm thinking this is why we'll never find an herbivore race reaching intelligence and civilization in the galaxy. They get stuck in this anarchistic zero-cooperation state.
To be fair that isn't entirely lossy either in its natural environment. "Wastage" of fruit leads to accidental plantings which leads to some more in the future. Just look at how squirrel stashes have turned into accidental tree farming as unretrieved stashes germinate.
Buffalo being hunted almost to extinction wasn't a case of tragedy of the commons, it was part of a deliberate policy to drive Native Americans from the land.