I would paradoxically recommend a book that I did not have opportunity to read so far. Not that I would not want to. It is The evolution of cooperation by Robert Axelrod (or the article from Science with the same name by Axelrod and Hamilton). It is an older work but based on the reviews, it is supposed to be an interesting reading with interesting conclusions.

Tomas responded with an interesting take that ducks signal out of group cooperation. Sounds convincing but I would be interested in reading more. It does make sense that repeated group interaction would produce cooperation.

It is a big world for a little duck and so the ducks must stick together to survive. Let`s say that the probability of finding the food is equal for all ducks, but some ducks have more luck one day and some on the other day. Sharing the food doesn’t change the total income of food of one duck but it changes the way how food is devided in time. Let’s suppose there are 10 ducks in a flock and each finds food of quantity 1 with the probability of 5%. If the ducks eat only their own food, they eat 1 food every 20th day. If they share the food, they eat every day on average one 20th of the whole portion. If one 20th is enough for a comfortable living, it is for sure better than the other alternative. It is even better in case a duck cannot last 20 days without eating something.

Of course in the case of a famine the situation is different. The probability of finding food would be much lower. If it is so low that the portion of food a duck gets when sharing is not sufficient to survive a longer period than the period between eating the whole portion and dying, quacking doesn´t make sense anymore. So in the case of a famine the uncertainty about the future makes the duck-dinner into a one-shot game and the manners of ducks probably change.

So according to these computations it is better to signal the presence of the food from a long-term perspective because then the duck can expect the others to do so as well. If a duck-dinner was a oneshot game as in the case of a famine, it would be rational to betray the flock and not to quack. But an empirical evidence through experiment would be too cruel, so we may never uncover the true nature of ducks’ character.

This is fine when an abundance of food is available. But what happens during a famine?

I mean if you where a duck and found some food, wouldn’t you be better off being silent, gorge yourself, listen carefully for any quacks, and then fly off to get your fair share?

I’ve never meet a silent duck on our lake, they all seem to quack. So how do they do it?

Michael Webster:
This is very interesting, the concept of probability matching. I have to read up on more beyond the sports applications I know about.