Game Theory

Non-Zero-Sum Games

To understand non-zero-sum games, it is helpful to give an example of the opposite: a zero-sum game.

Here’s a fun game: “stealing your older brother’s ice cream”

The little brother is unhappy because he has no ice cream, so he has a utility score of -1. “Utility” is a term economists sometimes use to roughly measure happiness.

The older brother is happy because he has ice cream, so he has a utility score of 1.

Together, their collective welfare is equal to 0.

After a change in the allocation of goods, their total welfare has not increased, it is still zero.

In a zero-sum game, the total amount of wealth remains the same and it is just a question of how you divide up a fixed pie, or ice cream cone.


 

 

 

 

 

 
 
 

In a NON-zero-sum game, the choices people make actually affect the total wealth in the system.  I will illustrate this with the crepes-Nutella environment in the Gains from Exchange chapter.

Let’s say that, due to sea weather conditions, each island can only send one boat on the first day of every month, and they will not know if the other island sent a shipment of food until that boat arrives two days later.  So, on the first day of each month, both islands have two strategies to chose from: { send, don’t send }.

Economists sometimes present these games using a payoff matrix:

North Island
Send Don’t Send
South Send 6, 6 2, 7
Don’t Send 7, 2 3, 3

The pair of numbers {x, y} in each box represent what the {South, North} would earn for each decision set.

If neither chose to send, they both are stuck with boring food.
3+ 3 = 6

If North island sends food and South island does not, the South will be better off but the North will have less noms than before.
7+ 2 = 9

If both chose to send, they will both get to enjoy delicious crepes with Nutella, resulting in an increase in total welfare.
6 + 6 = 12

Posted in Non-Zero-Sum Games | 1 Comment