Game Theory: Non-Zero-Sum Games
In non-zero-sum games, one player's gain does not have to be another player's loss.
- Everyone can win, or everyone can lose, at the same time!
- Working together often brings the best results for all
These games happen a lot in real life. You see them in business, nature, and even how we protect our planet. They show us that helping others can also help ourselves.
Let's look at a classic story to see how this works.
The Battle of the Sexes
Alex and Taylor want to hang out tonight, but they like different things:
- Alex wants to go to a concert. Taylor wants to see a movie
- If they go alone, they feel lonely
- If they go together, they are both happy, even if the activity wasn't their first choice!
The numbers below show "happiness points." Bigger numbers mean more smiles!
… think for a second: what would you tell them to do? …
Talking it out is key. In these games, a little chat can help everyone get a better deal.
Their choices look like this:
The first number is Alex's happiness, the second is Taylor's.
The key idea is that choosing to be together gives better results than going alone.
A Cooperative Strategy helps both people:
- They could take turns choosing each week
- This keeps things fair and keeps the points high for all
Nash Equilibria in This Game
In this game, there are outcomes where neither Alex nor Taylor can improve their happiness by changing their choice alone. These outcomes are called Nash Equilibria.
In this example, (Concert, Concert) and (Movie, Movie) are both Nash Equilibria. Once one of these choices is made, neither person benefits from switching on their own.
The challenge isn't whether an equilibrium exists, but which one they will choose. Real-life solutions often depend on trust, fairness, and communication.
Example: Two Companies
- TechCo and BizCorp can choose to work together or compete for customers
- If they work together, they both make good money
- If they compete, they spend so much on ads that they both lose money!
The possible outcomes are:
This is a non-zero-sum game because both companies can gain together, or lose together. But it takes trust. If one tries to be nice and the other attacks, the nice person loses big!
More Than Just Winning
These games prove that you don't have to beat someone else to "win."
Cooperation can lead to better outcomes for all rational players.
By looking for "win-win" spots, we find better ways to live and work together.
Why It Matters
Understanding non-zero-sum games helps us spot opportunities team up instead of arguing.
By thinking beyond "winning and losing," we can often find solutions where everyone does better.
Life isn't always about "me versus you." Often, it is "us versus the problem!"