What is the Nash Equilibrium?

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History

This game theory concept of Nash equilibrium is named after American mathematician John Nash, who was awarded the Nobel Prize in Economics in 1994 for his invaluable contribution to the field of game theory.

The underlying principle is similar to Antoine Augustin Cournot’s oligopoly theory (1838). As per Cournot’s theory, all the firms in a competitive market would choose to produce only that much output to maximize their profit. However, the best output of one firm is dependent on the output of the others in the market. Consequently, Cournot equilibrium is achieved only when each firm’s output maximizes its profits, taking into account the output of the other firms, which is again the strategy for Nash equilibrium.

The modern concept of Nash equilibrium game theory has changed a bit. It also includes mixed strategies, wherein the participants avert possible actions and prefer to choose probability distributionProbability DistributionProbability distribution could be defined as the table or equations showing respective probabilities of different possible outcomes of a defined event or scenario. In simple words, its calculation shows the possible outcome of an event with the relative possibility of occurrence or non-occurrence as required.read more. Oskar Morgenstern and John von Neumann pioneered this mixed-strategy concept under Nash equilibrium in their book The Theory of Games and Economic Behavior (1944).

Examples of Nash Equilibrium

Example #1

X Co. and Y Co. illustrate the concept of Nash equilibrium in game theory. Both companies intend to determine the right time to expand their production capacity. If both companies expand their capacities now, each can increase their market shareMarket ShareMarket share determines the company’s contribution in percentage to the total revenue generated within an industry or market in a certain period. It depicts the company’s market position when compared to that of its competitors.read more by 10%. However, if only one of them decides to expand, it can increase its market share by 20%, while the other will not gain any market share. On the other hand, if both companies give up the idea of expansion, neither will gain any market share. The below table indicates the payoff in this case.

So, in this case, the Nash equilibrium is achieved when both companies expand their production capacities as it offers a better payoff overall.

Example #2

Let us look at another example to illustrate the concept of multiple Nash Equilibria in game theory. Imagine that two friends, David and Neil, are registering for a new semester. They both have the option to choose between finance and marketing. If David and Neil register for the same class, they can study together for the exams. But, on the other hand, if they pick different classes, they will neither lose out on the mutual benefit of group study. The below table indicates the payoff in this case.

So, in this case, multiple Nash equilibria are achieved when David and Neil register for the same class. Thus, the outcomes are David picks finance – Neil picks finance, and David picks marketing – Neil picks marketing.

Applications

  • Analysis of hostile situations like arms races, and wars (Prisoner’s dilemmaPrisoner’s DilemmaThe prisoner’s dilemma refers to a paradox in the decision-making and modern game theory that exemplifies how two rational individuals trapped in the same situation are likely to respond to it without knowing other’s take on the same. They either act in their self-interests or refuse to cooperate, leading to a sub-optimal or non-optimal outcome.read more).Analysis to mitigate conflict through repeated interactions.Study human behavior to determine when people with different preferences can cooperate.Determination of probability of currency crises and bank runs (Coordination game).Design algorithm for traffic control (Wardrop’s principle).

Advantages

  • It is a well-defined quantitative approach to decision-making in a competitive situation.It helps in the assessment of the competitors’ reactions.It is a management tool that helps in policy making.

Disadvantages

  • Determining the optimal solution becomes difficult with the increase in participants.It is more of a logical strategy and not a winning strategy.The concept fails to account for uncertainties encountered in real-life business situations.The theory expects the participants to act rationally, which is not always the case.

This article is a guide to What is Nash Equilibrium Game Theory and its definition. We discuss its history, examples, applications, advantages, and disadvantages. You can learn more about it from the following article:  –

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