Nash equilibrium

In game theory, the Nash equilibrium is a proposed solution of a non-cooperative game having two or more players in which each player knows the equilibrium strategies of the other players, and no player can gain anything more by changing only their own strategy. The equilibrium is named after John Forbes Nash Jr..

If each player has chosen, and no player can win anything more by choosing a different strategy for themselves, then they have a Nash equilibrium.

Nash Equilibrium Media

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  Sample network graph. Values on edges are the travel time experienced by a "car" traveling down that edge. x is the number of cars traveling via that edge.

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  Extensive and normal-form illustrations that show the difference between SPNE and other NE. The blue equilibrium is not subgame perfect because player two makes a non-credible threat at 2(2) to be unkind (U).