Nash equilibrium (definition and characteristics)

Before talking about Nash equilibrium, let's get to know a little about the creator of him, John forbes nash, a mathematician born in 1928, studied at Princeton, was a mathematical genius who despite suffering from paranoid schizophrenia, surpassed the expectations of many, so that in 1994 he was awarded the Nobel Prize in economics, he died at the age of 84, in a car accident. transit.

One of the most outstanding contributions of him is the Nash equilibrium, from the year 1951, of a multidisciplinary nature, with this theory he demonstrated that any situation where decisions would have to be made, constitutes a game of strategies that allows considering several options for make a decision.

What is the Nash equilibrium?

Known as the games theoryIt is a problem-solving conception, it incorporates a variable scenario, under which both the different elements involved obtain the best benefits. Determined by the different options that the possible choices represent, of one of the elements, depending on the decisions that the other element involved has to make.

It is essentially based on the following principles:

• Principle of rationality, based on the reasoning capacity of people, at the time of solving problems, this means that, if there are two possible solutions to a problem, it is sought to make the best decision to solve the problem. trouble.
• Principle of common knowledge of rationality, states that a solution to a problem will be accepted and consequently supported on the contrary.

There are usually two positions, which generate a Balance, but it is always necessary to evaluate which of the two options generates better benefits.

Nash equilibrium applications:

• In real and simple circumstances of life.
• In mathematics, that's why game theory is known.
• On economy, in economic terms was developed and applied by Antonie Augustin Cournot, in his analysis regarding the known economic models of Oligopolies. Under this modality, said economist raises the competitiveness between several companies, all for obtaining the same purpose with the same good, each one of them trying to obtain the ideal quantity to produce and thus increase its profit margin.

Nash equilibrium in the economic realm

Practical example of the Nash equilibrium.

A hotel chain is thinking of expanding its provision of services by incorporating the rental for conventions in one of its branches. There are two options here: “accept” or “no accept ”, based on this decision, a fast food franchise is studying the possibility of opening a branch in the same location as the hotel, if said hotel decides to open the room to conventions, the best option for the fast food franchise is to open the branch, since it could attract the public attending the conventions, which would imply a benefit for both Business.

Otherwise, if the hotel does not accept to hold conventions, it is better for the franchise not to open this new branch as it could not generate the expected income.

Nash equilibrium according to Cournot's proposals

Cournot developed the Nash equilibrium, as follows:

• Pure strategies dominant strategies.

According to this theory, the players, entrepreneurs or those involved, lose or win inversely proportional to the profit or loss of their opponent, that is, everything that a businessman or player wins or loses is equivalent to what his opponent loses or wins, thus remaining unchanged the economic situation at the level global.

• Mixed strategies

It results from the combination of different action strategies, among the main ones are those developed by Modern Game Theory, whose authors are Oskar Morgenstein and John Von Neuman.

Characteristics and application of the Nash Equilibrium

The assumptions that allow us to reach the Nash equilibrium are the following:

• Those involved in the situation or in the game want to maximize their income and therefore expect a profit according to the conditions determined in the situation.
• The players or those involved study the environment of the situation very well and apply strategies deliberately with the slightest margin of error.
• Those involved possess sufficient knowledge to determine their own balances and those of their opponents.
• Each individual also determines his path according to the decisions that his opponent decides.
• It is expected that, even if one of the individuals modifies her strategy, this decision will not affect the decision of the other involved.
• All the agents or elements involved that interact assume the commitment to assume and respect the rules established and at the same time rationality is expected as a habitual characteristic of each and every one of the involved.
• If only one of the players or the slopes does not apply the principle of rationality, the Nash equilibrium is immediately lost.
• If only one of those involved does not have a strategy to apply, the Nash equilibrium.