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Nash equilibrium

Some games have dominant strategy and dominant strategy equilibrium, and some games do not have dominance

What is Nash Equilibrium

Two people game

There is no dominant strategy on either side of the game, that is, there is no dominant strategy equilibrium


B 1 B_1
B 2 B_2
B 3 B_3

A 1 A_1 		13, 13 7, 14 8, 12

A 2 A_2 		14, 7 12, 12 7, 13

A 3 A_3 		12, 8 13, 7 11,

(A3,B3)(A_3,B_3)(A3,B3) is the Nash equilibrium of the game. If there are two strategies (or more strategies, each strategy corresponds to one player) and each strategy is the optimal response of another strategy (or strategies of other players), the strategy combination is called Nash equilibrium strategy combination.

If a game has a combination of Nash equilibrium strategies and players choose those strategies, a ** Nash equilibrium * is obtained for the game

So the Nash equilibrium, the Nash equilibrium, is a set of strategies in which none of the players would benefit from changing their strategies alone.

The strategy combination is the Nash equilibrium (point) of the Nash game. At the Nash equilibrium point, all players are faced with such a situation that their strategy is the best when other players do not change their strategy.

The perinatal period remains stable, adheres to the original principle of maximizing benefits, and rationally faces the reality.

  • Nash equilibrium is a stable and predictable interaction between players in a game. Introduction to finding Nash

  • Optimal response strategy,

  • Underline the payoff number corresponding to the optimal response strategy of each strategy in the payoff matrix, if in a box

conclusion

  • A Nash equilibrium refers to a combination of strategies that are optimal for all players
  • That is, at the Nash equilibrium, each rational player will not change the strategy impulse alone, because it is impossible for any player in the game to increase their returns by unilaterally changing their strategy.
  • Nash equilibria are not dominant strategy equilibria, they are non-cooperative equilibria