Nash Equilibrium (NE)
- 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
- Nash showed that there is a Nash equilibrium for every finite game
NE - Example
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.