Game Theory: Non-Zero-Sum Games
In non-zero-sum games one player’s gain does not have to mean another player’s loss.
- It is possible for all players to benefit, or lose, together
- Working together can often lead to better results for all
Games like this are common in economics, business, environmental planning, and many real-life situations where working together can improve results for everyone.
Let's explore an example to see how non-zero-sum games work and how cooperation can lead to better outcomes.
The Battle of the Sexes
Alex and Taylor want to spend the evening together, but they have different preferences:
- Alex prefers going to a concert, while Taylor prefers a movie
- If they go separately, neither enjoys the evening much
- If they go together both are happier, even if it is not their first choice
The numbers below represent how happy each person is. Higher numbers mean greater satisfaction.
… take a moment to think: what would you suggest they do? …
In non-zero-sum games, communication and cooperation often lead to better solutions. If Alex and Taylor can talk things through, they may realize that compromising makes them both happier.
Their decision table looks 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.
Cooperative Strategy recognizes both preferences:
- They might take turns choosing where to go
- Over time, this maximizes happiness for both
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 is not whether an equilibrium exists , but which one they will choose. Real-life solutions often depend on trust, fairness, and communication.
Example: Corporate Collaboration
- Two companies, TechCo and BizCorp, are deciding whether to collaborate or compete
- If they collaborate, both earn strong profits
- If they compete, high costs reduce profits for one or both companies
The possible outcomes are shown below:
This is a non-zero-sum game because both companies can gain together , or lose together. Mutual collaboration produces the best result for both.
This requires trust. If TechCo tries to collaborate but BizCorp competes, TechCo loses money while BizCorp takes the market share.
Beyond Competition
Non-zero-sum games show that competition is not the only path to success.
Cooperation can lead to better outcomes for all rational players.
Unlike zero-sum games, where one player's gain is another's loss, non-zero-sum games allow solutions where everyone can benefit.
Why Non-Zero-Sum Games Matter
Understanding non-zero-sum games helps us recognize opportunities for partnership, negotiation, and cooperation in everyday life.
By thinking beyond "winning and losing," we can often find solutions where everyone does better.