A pair of pigs, one dominant and one subordinate, are in a box and have a chance to be rewarded with food. At one end of the box is a lever which releases food when pressed. The twist is the food is released at the other end of the box. The pig that presses the lever is at a disadvantage as the other pig can get to the food first.
We can model the game using some numbers. If the dominant pig presses the lever, the subordinate pig can eat 80 percent of the food before the dominant pig can arrive and take the rest. If the subordinate pig presses the lever, then the dominant pig can take all the food as the subordinate pig races across the box. If neither pig presses the lever, then neither pig gets any food. And if both are adjacent when the lever is pressed, the dominant pig can eat 70 percent of the food.
Suppose the food is worth 10 units, it takes 1 unit of energy to press the lever and rush to the other side of the box to fight for the food. The game then has the following payouts.
How should the two pigs act if they reason like game theorists? Let’s solve this game and then see how pigs actually behave in an experiment.
Solving for the Nash equilibrium
Consider the choice of the subordinate pig. If the dominant pig presses the lever, then the subordinate pig is better off not pressing the lever and raiding the food to get 8. If the dominant pig does not press the lever, then the subordinate pig is better not pressing, because it is better to get 0 than to get -1 from getting no food and expending energy.
Notice the subordinate pig has a dominant strategy of not pressing the lever. These best responses are depicted by overlines in the appropriate cells of not pressing the lever.
What should the dominant pig do? For completeness, let us consider each choice of the subordinate pig. If the subordinate pig presses the lever, the dominant pig would rather not press the lever and get all 10 units of food. If the subordinate pig does not press the lever, then the dominant pig should press the lever to get a payoff of 1 versus a payoff of 0 for not pressing.
These best responses are depicted by underlines in the appropriate cells.
The unique Nash equilibrium of this game is the cell with both an overline and an underline, in which both pigs are playing a best response. This corresponds to the dominant pig pressing the lever, the subordinate pig not pressing the lever.
The subordinate pig gets 8 while the dominant pig gets only 1.
How pigs actually played
Baldwin and Messe did this experiment and published about it in 1979. While pigs do not actually write the matrix game and solve it, they can learn optimal behavior. The researchers found the dominant pigs did almost all of the pressing. In other words, the pigs acted just as game theory predicted they would! While pigs do not know game theory, there is a role of game theory to predicting animal behavior (read how dung flies optimally exit a war of attrition, for example).
The lesson: strength can be a weakness!
The game is also interesting from a business perspective. Typically we think dominance translates into strategic strength: the stronger animal should beat the weaker one. But in this game, strength is a weakness! The dominant pig ends up with almost no food compared to the subordinate pig.
Why is this happening? The strategic problem is the dominant pig is too dominant. If there is a fight for food, the subordinate pig knows that it will get nothing. So the subordinate pig never wants to waste time pressing the lever and fighting for the food.
As a consequence, the dominant pig settles for pressing the lever to get a little bit of food. The subordinate pig’s “protest” to not press the lever steals the power and overwhelms the physical strength of the dominant pig.
Baldwin, B. A., and G. B. Meese. “Social Behaviour in Pigs Studied by Means of Operant Conditioning.” Animal Behaviour 27 (1979): 947-957. https://www.researchgate.net/publication/256111949_Social_behaviour_in_pigs_studied_by_means_of_operant_conditioning
Post extract from Presh Talwalkar, MindYourDecisions channel on YouTube,