Business, Legal & Accounting Glossary
Nash Equilibrium (NE) is a game theory concept that illustrates the result of a particular game. Most fundamentally, NE is the result of a collection of decisions in which no player would like to change the result, holding all other decisions constant (because a player can only change his or her behavior).
Nash equilibrium, propounded by John Nash, is essentially a collection of game theory strategies that involves at least two individuals or players wherein no individual can make improvements on his or her payoff by making changes in strategy. Here each player’s strategy is an optimal response based on the expected strategy of other individuals or players. John Nash was awarded Nobel Prize for economics in 1994 together with Reinhard Selten and John Harsanyi for their analysis of equilibrium in non-cooperative game theory.
Nash theorem focused on mutual gains among rivals, is based on the ‘general equilibrium theory’ of Leon Walrus, and the theory of games established by Oskar Morgenstern and John von Neumann. Based on these, John Nash formed his dominant strategy equilibrium for sum zero games through solutions maximization. For establishing his theorem John Nash took the help of mathematical techniques.
In Nash equilibrium, players do not get incentives for deviating from their chosen strategy since they could not have chosen better strategies subject to the choices of other players.
John Nash’s equilibrium theorem explains the behaviour of small groups operating in an economic environment. It has become a tool for determining modern market behaviour, individual behaviour, and complex strategic environments.
One way to find Nash equilibrium is to examine each possible outcome of a game (cells) and compare payoffs. If a player could get a higher payoff ceteris paribus, then that strategy is not Nash equilibrium.
Also, a NE is the outcome of a game where no player wants to unilaterally deviate. This is another way to say, she can only control her own behavior, not any other players. Also when working with Bayesian NE, remember to use the “INDIFFERENCE PRINCIPLE” which is to say at what point, given a probability P for action A, and probability 1-P for action B (assuming just 2 actions) would the player be indifferent between the 2 strategies. This is built off of expected utility from a strategy which COULD be a strategy from a set of strategy profiles.
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This glossary post was last updated: 22nd November, 2021 | 0 Views.