A Nash equilibrium is a solution in game theory where no player is better off changing their action, commonly used in economics. It can be seen in the example of two companies setting prices for the same product, but real-world conditions can complicate matters. Nash equilibria can force firms to compete in other ways, but not all outcomes offer the highest combined profits.
Named for economist and mathematician John Forbes Nash, Jr., a Nash equilibrium is a special kind of solution in game theory. Game theory itself is a type of applied mathematics, common in economics and other fields, in which the strategic behavior of two or more individuals or entities is captured mathematically. A Nash equilibrium is a situation where, given the actions taken by the other players involved in the competition, no player is better off changing their action. In economics, applications of a Nash equilibrium include the setting of prices between competing companies.
A Nash equilibrium can be seen in the example of a simple market where two companies sell the same product and have the same profit margin per unit sold. Essentially, in this example, their profits are determined by the number of products sold, which is determined by the price. If companies have the choice to set their price at $1 US Dollar, $2 USD, or $3 USD, the best price for each company will be influenced by the price set by the other company. A Nash equilibrium will be reached when neither company will benefit from the change in its price unless the other company also changes its price.
If, in this example, both companies set a price of $3 USD, each company might have an incentive to reduce its price if the other company keeps its price at $3 USD, provided the lower revenue per unit is more than offset by increased sales. In that case, the total profit for that company will increase, while the total profit for the company that kept the same price will likely decrease due to a decrease in sales. If both companies set a price of $2 USD, each will have the incentive to lower the price to $1 USD for the same reason. If both companies set a price of $1 USD in this example, a Nash equilibrium will be reached, since neither company will have an incentive to increase its price if the other company keeps its price at $1 USD. In this example, if a company raised its price to $2 USD, its reduction in sales would more than offset the increase in per-unit revenue, and the company’s total profit would decrease.
In the real world, conditions are much more complex than in this simple example. It can be difficult to determine whether a change in price and subsequent change in the number of products sold will increase or decrease total profits. Other conditions that might come into play are things like markets with more than two competing companies, overlapping markets, and similar but not identical product effects.
When a Nash equilibrium is reached and none of the competing firms have an incentive to change its price, it often forces the firms to compete in other ways. For example, a company may be able to increase its profits by reducing operating and manufacturing costs. Companies may also be forced to produce a better product or come up with other innovations.
There are a few things to note about Nash equilibria. Any competitive market may have no Nash equilibria, one Nash equilibrium, or multiple Nash equilibria. It’s also important to note that while each firm is making the best possible choice given the choices of its competitors, not all Nash equilibrium outcomes offer the highest combined profits to the firms involved. There are often cases where combined profits could be higher if the companies could agree to change their shares and cooperate, but this behavior is often prohibited by antitrust legislation intended to promote competition between companies.
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