History of Nash Equilibrium: Discovery and Use Today
Overview
Discovered by American mathematician, John Forbes Nash, Jr., Nash equilibrium is a fundamental concept in game theory that illustrates decision-making in players based on their interactions with others. The main purpose is to optimize a player’s outcome by taking into account other players’ decisions. Nash equilibrium is achieved when neither player—in a two player game—has any incentive to deviate from their strategy. This holds true even when both players know the other’s strategies. By using Nash equilibrium, we can model economic behaviors and predict best responses to given scenarios.
John Forbes Nash, Jr. and Nash Equilibrium
Regarded as one of the greatest mathematicians of the 20th century, John F. Nash, Jr. was a genius when faced with mathematics. He was known for his originality and boldness when facing seemingly unsolvable problems. Throughout his life and career, he introduced numerous concepts that are now central to game theory and mathematics. He first began his work on equilibrium theory during his time at Princeton University while pursuing graduate studies in mathematics and sciences. In 1950, he earned a PhD with his 27-page thesis on non-cooperative games which provided a way to predict game outcomes while maximizing self-interest: Nash equilibrium. This dissertation contained the definition and use of the Nash equilibrium which is crucial to understanding non-cooperative games. 44 years later, he received the Nobel Memorial Prize in Economic Sciences for his work in game theory. This single concept has greatly changed the analysis of competitive situations. Roger Myerson, an economist at the University of Chicago, compared the impact of the discovery of Nash equilibrium to that of “the discovery of the DNA double helix in the biological sciences.” From business rivalries to policy-making, Nash equilibrium has become instrumental in the social sciences and continues to make headway in other fields.
Before Nash and game theory, economics was largely based on the theory of supply and demand and Keynesian economics. However, this could only be broadly applied to the dynamics of markets with many buyers and sellers. The dynamics of particular industries and businesses still lacked in theory and research. When examining how competition existed between businesses or how bidders decided to bid, economists had little progress. The first people to develop game theory were von Neumann and Oskar Morgenstern. They provided the framework for analyzing such situations, but they were only able to determine “equilibria” for situations with a definite winner and a definite loser. This failed to apply to real world situations where a definite winner or loser often did not exist. Instead, multiple competitors could have positive payoffs depending on the strategies they used. Nash began developing his equilibrium theory by starting out with a solution to games where each player performs the best to their ability, given the strategies of other players. Using his solution and the mathematical theory developed by L. E. J. Brouwer, a Dutch mathematician, Nash was able to demonstrate that his theory of equilibrium existed in any game with finite players and strategies. Despite being dismissed by von Neumann, Nash’s theory of equilibrium became one of the most widely known concepts in game theory and economics. To this day, students and economists alike use Nash equilibrium to solve for best responses and rule out illogical answers. As research continues in different fields, Nash equilibrium may eventually extend well beyond its current applications in economics.