Game theorists use the Nash equilibrium concept to analyze the outcome of the strategic interaction of several decision makers. In other words, it provides a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the outcome depends on the decisions of the others. The simple insight underlying John Nash’s idea is that one cannot predict the result of the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others.Nash equilibrium has been used to analyze hostile situations like war and arms races (see prisoner’s dilemma), and also how conflict may be mitigated by repeated interaction (see tit-for-tat). It has also been used to study to what extent people with different preferences can cooperate (see battle of the sexes), and whether they will take risks to achieve a cooperative outcome (see stag hunt). It has been used to study the adoption of technical standards, and also the occurrence of bank runs and currency crises (see coordination game). Other applications include traffic flow (see Wardrop’s principle), how to organize auctions (see auction theory), the outcome of efforts exerted by multiple parties in the education process, regulatory legislation such as environmental regulations (see tragedy of the Commons), and even penalty kicks in soccer (see matching pennies).
Year 91 – 1951: “Non-cooperative Games” by John Nash, in: Annals of Mathematics 54 (2) | 150 Years in the Stacks – The foundational game theory work of mathematician John von Neumann and economist Oskar Morgenstern, published in 1944, provided a framework for solutions to zero-sum games, where one player’s win was the other’s loss. Nash, in his dissertation research at Princeton (published in this and three other papers), extended game theory to n-person games in which more than one party can gain, a better reflection of practical situations. Nash demonstrated that “a finite non-cooperative game always has at least one equilibrium point” or stable solution. This result came to be called the “Nash equilibrium,” a situation where no one player can get a better payoff by changing strategies, so long as other players also keep their strategies. Using Nash’s framework, predictions can be made about the outcomes of strategic interactions.
— A Brief Introduction to NON-COOPERATIVE GAME THEORY – Like most really powerful ideas, the basic notion of Nash equilibrium is very simple, even obvious. Its mathematical extensions and implications are not, however. The idea of this natural “sticking point” is that no single player can benefit from unilaterally changing his or her move — a non-cooperative best-response equilibrium. Competitive Markets come to rest at Nash equilibrium, and the special structure of competitive markets makes them efficient. (As we will see in another game.) But it is important to recognize that MOST Nash-Equilibria are NOT efficient. What do we mean by not efficient? It’s just the idea of getting the “whole pie” — that if we’re really using the whole pie, then no one can get any more unless someone else takes less. That’s the economist’s basic idea of allocative efficiency. A famous game is called “Chicken,” named after a famous adolescent hot-rod ceremony from the United States of the 1950s. Say that Boeing and Airbus are both considering entering the jumbo jet market, but that because of increasing returns to scale and relatively low demand, there is only enough room for one of them. The game matrix (called the “normal form” of a game) could look like this. (This example is taken from an article by Paul R. Krugman, “Is Free Trade Passe?” in the Journal of Economic Perspectives, Fall 1987.)