Why Is the Nash Equilibrium So Important?

Quora
The best answer to any question.
July 16 2014 7:39 AM

Why Is the Nash Equilibrium So Important?

53001204-nobel-prize-laureate-john-forbes-nash-of-usa-listens
Nobel Prize laureate John Forbes Nash in Beijing in 2005.

Photo by China Photos/Getty Images

This question originally appeared on Quora.

Answer by Balaji Viswanathan, currently working on From Tryst to Tendulkar: The History of Independent India:

Advertisement

Game theory is a study of strategies involved in complex games. Almost every human interaction—politics, economics, law, and religion—can be modeled as a game. You are in a game if your fate is impacted by the actions of others.

There are many ways to classify the games. One such classification is whether the game is cooperative. Cooperative games are like partnerships where the players work together and contracts can be used for noncooperative players.

Noncooperative games are those where the players enter into no agreement and each one is looking after his or her own interests. Think of Apple versus Google or U.S. versus Russia. They are playing a complex game.

What John Forbes Nash Jr. said in his landmark work—“Equilibrium Points in N-Person Games”—is that even in such complex noncooperative games there exists an “equlibrium” where no side would benefit by changing its course. At this equilibrium, each sides knows its adversary very well and sticks to its strategy. For instance, during the Cold War, the U.S. and USSR were locked into an equilibrium—mutual assured destruction—where each side knew exactly where the other's positions are but still didn't start a war.

Suppose my wife and I are trying to coordinate when to reach home. If I go home and she is late, then I waste time. If she goes home and I'm late, she wastes time. The Nash equilibrium occurs when both of us reach home early, enabling us to spend time together, or both of us work late, making more money. These two circle points are the Nash equilibria. 

qur_140716_gametheory
This payoff matrix shows how many points each player gets if a particular strategy is taken. For instance, if a husband and wife both go home early (top-left quadrant), both get three points. If the husband works late and the wife goes home, the husband get two points, while the wife gets only one, as she is bored.

Courtesy of Balaji Viswanathan

By mathematically proving that there exists at least one such equilibrium point in any such game, Nash helped economists, politicians, bureaucrats, and business strategists understand the world around us in a better way. It formed the basis of many strategies we see around the world. It also indirectly showed how different players can dance to the tune even without the need for contracts.

There can be multiple equilibria in a game. Each equilibrium point is like a lock out of which no player will be able to escape easily. For instance, India and Pakistan can fight each other like cats and dogs to infinity or an equilibrium where they can collaborate in a virtuous loop. When the players are locked into a bad position (such as an arms race), it is called the Pareto inferior equilibrium.

To sum it up, the simplicity of Nash equilibrium enabled the growth of game theory as a legitimate discipline and enabled strategists and regulators to better model their environments.

More questions on Quora:

TODAY IN SLATE

Culturebox

The Ebola Story

How our minds build narratives out of disaster.

The Budget Disaster That Completely Sabotaged the WHO’s Response to Ebola

PowerPoint Is the Worst, and Now It’s the Latest Way to Hack Into Your Computer

The Shooting Tragedies That Forged Canada’s Gun Politics

A Highly Unscientific Ranking of Crazy-Old German Beers

Education

Welcome to 13th Grade!

Some high schools are offering a fifth year. That’s a great idea.

Culturebox

The Actual World

“Mount Thoreau” and the naming of things in the wilderness.

Want Kids to Delay Sex? Let Planned Parenthood Teach Them Sex Ed.

Would You Trust Walmart to Provide Your Health Care? (You Should.)

  News & Politics
Politics
Oct. 22 2014 9:42 PM Landslide Landrieu Can the Louisiana Democrat use the powers of incumbency to save herself one more time?
  Business
Continuously Operating
Oct. 22 2014 2:38 PM Crack Open an Old One A highly unscientific evaluation of Germany’s oldest breweries.
  Life
Lexicon Valley
Oct. 23 2014 10:30 AM Which Came First, the Word Chicken or the Word Egg?
  Double X
The XX Factor
Oct. 23 2014 8:51 AM The Male-Dominated Culture of Business in Tech Is Not Great for Women
  Slate Plus
Tv Club
Oct. 22 2014 5:27 PM The Slate Walking Dead Podcast A spoiler-filled discussion of Episodes 1 and 2.
  Arts
Brow Beat
Oct. 23 2014 9:00 AM Exclusive Premiere: Key & Peele Imagines the Dark Side of the Make-A-Wish Program
  Technology
Future Tense
Oct. 22 2014 5:33 PM One More Reason Not to Use PowerPoint: It’s The Gateway for a Serious Windows Vulnerability
  Health & Science
Bad Astronomy
Oct. 23 2014 7:30 AM Our Solar System and Galaxy … Seen by an Astronaut
  Sports
Sports Nut
Oct. 20 2014 5:09 PM Keepaway, on Three. Ready—Break! On his record-breaking touchdown pass, Peyton Manning couldn’t even leave the celebration to chance.