Loading the player...

What is the 'Nash Equilibrium'

The Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash Equilibria or none at all.

Nash Equilibrium

BREAKING DOWN 'Nash Equilibrium'

Nash Equilibrium is named after its inventor, John Nash, an American mathematician. It is considered one of the most important concepts of Game Theory, which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves. The reason why Nash Equilibrium is considered such an important concept of Game Theory relates to its applicability. The Nash Equilibrium can be incorporated into a wide range of disciplines, from economics to the social sciences.

Nash Equilibrium

The Nash Equilibrium is the solution to a game in which two or more players have a strategy, and with each participant considering an opponent’s choice, he has no incentive, nothing to gain, by switching his strategy. In the Nash Equilibrium, each player's strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome they desire. To quickly test if the Nash equilibrium exists, reveal each player's strategy to the other players. If no one changes his strategy, then the Nash Equilibrium is proven.

For example, imagine a game between Tom and Sam. In this simple game, both players can choose strategy A, to receive $1, or strategy B, to lose $1. Logically, both players choose strategy A and receive a payoff of $1. If you revealed Sam's strategy to Tom and vice versa, you see that no player deviates from the original choice. Knowing the other player's move means little and doesn't change either player's behavior. The outcome A, A represents a Nash Equilibrium.

Prisoner's Dilemma

The Prisoner's Dilemma is a common situation analyzed in Game Theory that can employ the Nash Equilibrium. In this game, two criminals are arrested and each is held in solitary confinement with no means of communicating with the other. The prosecutors do not have the evidence to convict the pair, so they offer each prisoner the opportunity to either betray the other by testifying that the other committed the crime or cooperate by remaining silent. If both prisoners betray each other, each serves five years in prison. If A betrays B but B remains silent, prisoner A is set free and prisoner B serves 10 years in prison, or vice versa. If each remains silent, then each serves just one year in prison. The Nash equilibrium in this example is for both players to betray each other. Even though mutual cooperation leads to a better outcome, if one prisoner chooses mutual cooperation and the other does not, one prisoner's outcome is worse.

  1. Trembling Hand Perfect Equilibrium

    In game theory, an equilibrium state that takes into consideration ...
  2. Zero-Sum Game

    A situation in which one person’s gain is equivalent to another’s ...
  3. Economic Equilibrium

    A condition or state in which economic forces are balanced. These ...
  4. Reinhard Selten

    An economist and mathematician who won the 1994 Nobel Memorial ...
  5. Equilibrium

    The state in which market supply and demand balance each other ...
  6. Competitive Equilibriums

    An equilibrium condition where the interaction of profit-maximizing ...
Related Articles
  1. Investing

    Game Theory: Beyond the Basics

    Take your game theory knowledge to the next level by learning about the Nash Equilibrium.
  2. Insights

    The Basics Of Game Theory

    Here we take an introductory look at game theory and the terms involved, and introduce you to a simple method of solving games, called backwards induction.
  3. Insights

    Advanced Game Theory Strategies For Decision-Making

    The importance of game theory to modern analysis and decision-making can be gauged by the fact that since 1970, as many as 12 leading economists and scientists have been awarded the Nobel Prize ...
  4. Investing

    The Business Model Of Private Prisons

    How does the business model of private prisons work?
  5. Insights

    Will Gilead Make a Good Fit for Allergan? (GILD)

    Allergan made two recent acquisitions in the NASH diseases space, and Gilead’s strong NASH drug portfolio can fit well with these.
  6. Investing

    A New CEO Takes the Reins at CarMax

    CarMax (NYSE: KMX) is driving into September with a new executive at the wheel. Bill Nash began his reign as CEO at the beginning of the month, succeeding the freshly retired Tom Folliard. Nash ...
  7. Insights

    The Prisoner’s Dilemma in Business and the Economy

    The prisoner’s dilemma provides a framework for understanding how to strike a balance between cooperation and competition.
  8. Insights

    Former Convict? Become A Consultant

    Even convicted criminals are becoming consultants with Wall Street prison consulting.
  9. Insights

    Can Games Make You A Better Investor?

    As investing is a great example of an activity that draws on a wide range of mental and emotional skills, it is worth exploring how to improve this skill set.
  10. Investing

    Prison Stocks Soar Following Trump Election

    While shares of Corrections Corp of America (NYSE: CXW) and GEO Group (NYSE: GEO) were beaten down following the Justice Deptartment's recent decision to limit the role private prison operators ...
  1. What does the Nash equilibrium predict?

    Learn more about the famous Nash equilibrium, which is the revolutionary concept in game theory about the economics of human ... Read Answer >>
  2. How Does the Law of Supply and Demand Affect Prices?

    Learn how the law of supply and demand affects prices. Read Answer >>
  3. How does a monopoly contribute to market failure?

    Read a simple overview of the theory of market monopoly, where it originated and some contemporary challenges to the classical ... Read Answer >>
  4. How do I decide whether a credit card offer is a good deal or not?

    Discover the ways that externalities lead to market failure. Externalities are costs or benefits that go to a third party, ... Read Answer >>
  5. How is a market failure corrected?

    Find out how to think about market failures, how they tend to be corrected and different proposals about the best way to ... Read Answer >>
  6. How has the popularity of online gaming affected the internet sector?

    Discover how the increasingly popularity of online gaming has directly affected and fundamentally transformed the Internet ... Read Answer >>
Hot Definitions
  1. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  2. Perfect Competition

    Pure or perfect competition is a theoretical market structure in which a number of criteria such as perfect information and ...
  3. Compound Interest

    Compound Interest is interest calculated on the initial principal and also on the accumulated interest of previous periods ...
  4. Income Statement

    A financial statement that measures a company's financial performance over a specific accounting period. Financial performance ...
  5. Leverage Ratio

    A leverage ratio is any one of several financial measurements that look at how much capital comes in the form of debt, or ...
  6. Annuity

    An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income ...
Trading Center