Here's the premise. We make switches that the birds know how to press and understand that pressing causes actions. Easy enough. Then we hook the switches up to some sort of reward dispenser. Press button, get sunflower seed or almond. So far pretty simple. Then, we put the birds in a game-theoretic situation like the prisoners dilemma. If both birds press the left button, they both get the high reward (almond). If they both press the right button, they both get the low reward (sunflower seed). If one presses left and the other presses right, the left presser gets nothing and the right presser gets the highest reward (almond AND seed, oh wow).
Our first question is if the birds will converge upon the Nash Equilibrium for this game. There's a second, even more interesting question we want to answer. The birds are capable of talking to each other, but they don't have a general purpose language. So far as we can tell, their vocabulary consists of 2 squawks, 3 squawks, 5 squawks, and rarely 6 squawks. The possible signals the birds might send each other are arbitrary and meaningless in the context of this experiment, but they can signal each other. Thus the question becomes, will the birds invent a meaning for their squawks in order to cooperate at this game? Can the evolution of language be explained by simply trying to maximize payoffs in the presence of other birds trying to maximize payoffs?
Our third question is if the birds ever start lying to each other? If so, can I get the birds to manage my Diplomacy games for me?
To the extent that the whales clearly have a structured language, I suggest a way to decode it. Ask not what the generic patterns of whale sounds might be, but instead ask what payoffs the whales need to negotiate over. What positive sum behavior do the whales engage in that would be impossible without signaling?