This article is an excerpt from the Shortform book guide to "Algorithms to Live By" by Brian Christian and Tom Griffiths. Shortform has the world's best summaries and analyses of books you should be reading.

What is the “Nash equilibrium”? How do you calculate the Nash equilibrium?

One of the most important concepts in game theory is the “Nash equilibrium”—a theoretical game state in which every player is fully aware of their opponents’ strategies yet sees no need to change their own. The game becomes stable and unchanging because everyone has settled into the best possible strategy available to them. If you can calculate an equilibrium, you can predict the inevitable stable outcome of any game’s rules and incentives.

Keep reading to learn about the concept of the “Nash equilibrium” and how it is used in game theory.

## The Nash Equillibrium

Game theory is the mathematical study of competition between strategic decision-makers—people, computers, or even animals. In these competitions, each player is trying to maximize their benefits, but importantly, their behavior has a direct impact on the other players. This typically results in endless strategizing and re-strategizing as each player attempts to predict what the others will do, knowing that everyone else is trying to do the same thing.

The Nash equilibrium is a key concept in game theory; if you can calculate an equilibrium, you can predict the inevitable stable outcome of any game’s rules and incentives. Christian and Griffiths assert that this function makes knowledge of Nash equilibria invaluable to policymakers of all kinds who want to bring about positive changes to the status quo.

### Mutually Harmful Equilibria: The Problem Game Theory Can Solve

Christian and Griffiths detail one major type of problem that game theory is good at solving: mutually harmful equilibria. When the optimal strategy for each player causes more harm to others than it helps the one using it, the system incurs a collective loss. In this case, the current Nash equilibrium hurts all players involved

For example, bluefin tuna fishing has a mutually harmful equilibrium. This tuna makes valuable sashimi, so each fisher’s optimal strategy is to catch and sell as many tuna as possible. However, after years of overfishing, the tuna is in danger of going extinct—if it isn’t protected, it’ll disappear, harming all the fishers who used to profit from it.

Game Theory: The Nash Equilibrium Explained

### ———End of Preview———

#### Like what you just read? Read the rest of the world's best book summary and analysis of Brian Christian and Tom Griffiths's "Algorithms to Live By" at Shortform .

Here's what you'll find in our full Algorithms to Live By summary :

• How to schedule your to-do list like a computer
• Why making random decisions is sometimes the smartest thing to do
• Why you should reject the first 37% of positions in your job search

#### Darya Sinusoid

Darya’s love for reading started with fantasy novels (The LOTR trilogy is still her all-time-favorite). Growing up, however, she found herself transitioning to non-fiction, psychological, and self-help books. She has a degree in Psychology and a deep passion for the subject. She likes reading research-informed books that distill the workings of the human brain/mind/consciousness and thinking of ways to apply the insights to her own life. Some of her favorites include Thinking, Fast and Slow, How We Decide, and The Wisdom of the Enneagram.