Rational Pigs
In class, we learned not only to play dominant strategies when we have them but also to recognize when other players have dominant strategies.
In a famous experiment, psychologists Baldwin and Meese deprived pigs of food for 48 hours and then placed pairs of pigs--one big and one small--together into a pen. The pen was outfitted with a lever at one end and a trough at the other end. When a pig pressed the lever, food would be dispensed into the trough.
The psychologists observed that the big pigs almost always pushed the lever while the small pigs simply waited by the trough.
There is a sensibility to this outcome. If the small pig were to press the lever, it would be unable to push the big pig out of the way to access the food. By instead waiting by the trough, the small pig is able to access some of the food before the big pig pushes it out of the way. The small pig has a dominant strategy.
To see this, consider the trough as containing 10 units of food:
- If the big pig is at the food first, it eats all 10 units of the food.
- If the small pig is at the food first, it eats 6 units of the food before being pushed aside.
- If the pigs arrive at the trough at the same time, the big pig gets 7 units of food, and the small pig gets 3.
This yields the following game:
| Big Pig | |||
|---|---|---|---|
| Press | Wait | ||
| Small Pig | Press | 1 , 5 | -2 , 10 |
| Wait | 6 , 2 | 0 , 0 | |
The pigs were first introduced to the pen separately to allow them to learn the relationship between pressing the lever and receiving food in the trough. Then, the pairs of pigs were placed together.
Here are the results from the original paper:
The big pig doesn't have a dominant strategy. If it expects the small pig to Wait, it should Press and if it expects the small pig to Press, it should Wait. Yet, the big pigs quickly learned to go straight to the lever each time. Apparently, the big pigs realized that the small pigs have a dominant strategy to Wait which left the big pigs with little choice but to Press the lever.
Source: Baldwin, B.A. and Meese, G.B., 1979. Social behaviour in pigs studied by means of operant conditioning. Animal Behaviour 7, 947-957.
Image adapted from cover of Wang Chun Yong, 2011, Game Theory in Our Daily Life-revised illustrated edition (Chinese Edition), China Development Press, ISBN 978-7802343863.