Definitions for nash equilibrium
nash equi·lib·ri·um

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Nash equilibriumnoun

   (game theory) a stable state of a system that involves several interacting participants in which no participant can gain by a change of strategy as long as all the other participants remain unchanged

WiktionaryRate this definition:0.0 / 0 votes

1. Nash equilibriumnoun

   The set of choices of players' strategies for which no player can benefit by changing his or her strategy assuming that the other players keep theirs unchanged.

2. Etymology: Named after the American mathematician

WikipediaRate this definition:0.0 / 0 votes

1. Nash equilibrium

   In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.If each player has chosen a strategy – an action plan based on what has happened so far in the game – and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice choosing A. In a game in which Carol and Dan are also players, (A, B, C, D) is a Nash equilibrium if A is Alice's best response to (B, C, D), B is Bob's best response to (A, C, D), and so forth. Nash showed that there is a Nash equilibrium for every finite game: see further the article on strategy.

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1. nash equilibrium

   Nash equilibrium, named after mathematician John Nash, is a concept in game theory where each player's strategy is optimal given the strategies of all other players. No player has anything to gain by unilaterally changing their strategy, assuming the other players keep theirs unchanged. It's a state of stable strategy profile where no player would benefit from changing their strategy while the others keep theirs constant.

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1. Nash equilibrium

   In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. Stated simply, Amy and Wili are in Nash equilibrium if Amy is making the best decision she can, taking into account Wili's decision, and Wili is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.

Matched Categories

1. • Equilibrium
   • Game Theory

How to pronounce nash equilibrium?

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Numerology

1. Chaldean Numerology

   The numerical value of nash equilibrium in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of nash equilibrium in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=nash equilibrium
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Nash_Equilibrium
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Nash_Equilibrium
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=nash equilibrium