Nash Equilibrium

A Nash Equilibrium is a Non-Cooperative Game Solution Concept in which each game player is assumed to know the equilibrium strategies of the other game players, and no game player can gain by changing their game strategy.

• Context:
  • It can range from being a Weak Nash Equilibrium to being a Strong Nash Equilibrium.
• Example(s):
  • a Coordination Game, where ...
  • a Prisoners Dilemma Game, where ...
  • …
• Counter-Example(s):
  • a Ocean Fishing Game.
• See: Experimental Economics, Rationalizability, Epsilon-Equilibrium, Correlated Equilibrium, Evolutionarily Stable Strategy, Subgame Perfect Equilibrium, Perfect Bayesian Equilibrium, Trembling Hand Perfect Equilibrium, 2nd Bid Auction.

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References

2016

• http://www.economist.com/blogs/economist-explains/2016/09/economist-explains-economics
  • QUOTE: This simple concept helps economists work out how competing companies set their prices, how governments should design auctions to squeeze the most from bidders and how to explain the sometimes self-defeating decisions that groups make. … The Nash equilibrium helps economists understand how decisions that are good for the individual can be terrible for the group. This tragedy of the commons explains why we overfish the seas, and why we emit too much carbon into the atmosphere. Everyone would be better off if only we could agree to show some restraint. But given what everyone else is doing, fishing or gas-guzzling makes individual sense.

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Nash_equilibrium Retrieved:2015-5-17.
  • 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 their own strategy. 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 constitutes a Nash equilibrium. The reality of the Nash equilibrium of a game can be tested using experimental economics method.

    Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can , taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long the other party's decision remains unchanged.

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