Nash Equilibrium and cooperative games: example

A lot of people have heard of Nash Equilibriums and cooperative games, but don’t understand why and how they are so powerful and useful. John Forbes Nash’s major contribution to game theory was showing how cooperation can yield better results than competition, overturning conventional economic notions that competition and the so-called ‘invisible hand’ always yields optimal results.

Here’s a really simple real-world example that shows how much superior cooperation is compared competition in terms of benefiting all parties:

Suppose you have 10 competitors that are vying for 10 markets. These competitors are are equal ability. In each market, there is a single customer. So if each of the 10 competitors is competing in each of these markets, and assuming equal skill, then each has a 1/10 chance of getting the customer. Across all the markets, combined, each competitor can expect single sale. But competing costs money. If a sale produces 1 unit of ‘utility’ but competing (such as marketing) costs 1/10 a unit, each competitor will break-even. Now suppose, instead, all 10 competitors hold a meeting and divide the 10 parcels evenly. Now each gets the customer, hence a single unit, and none of them have to spend anything on competing with each other. So they go from earning zero units, to each earning one, which is way better not only in terms of making more money but also requiring much less effort.

The downside is, because no one has to compete, there may be less innovation, because innovation is often borne out of competition. It also requires that all the parties communicate and not defect. It also makes the unrealistic assumption about skill levels being equal. If one competitor is much more skilled, then he has no incentive to cooperate. In the real world, skill is not additive, meaning that someone being 2x as skilled as someone else is not the same as two lesser-skilled people working together. In the real world, skill comes from proprietary knowledge–it is knowing some subtlety that gives one a major edge over the competition, even if both players are otherwise pretty much the same.