# Answer to Question #51181 in Microeconomics for zem lotjem

Question #51181

(a) Distinguish between pure strategy Nash equilibrium and mixed strategy equilibrium.

When would you use mixed strategy equilibrium?

(b) Find all the Nash equilibrium of the following game:

Player1

Player 2

Left Right

Up (5,4) (1,3)

Down (4,1) (2,2)

When would you use mixed strategy equilibrium?

(b) Find all the Nash equilibrium of the following game:

Player1

Player 2

Left Right

Up (5,4) (1,3)

Down (4,1) (2,2)

Expert's answer

(a) A game can have either a pure-strategy or a mixed Nash Equilibrium. (In the latter a pure strategy is chosen stochastically with a fixed probability). Nash proved that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.

(b) The Nash equilibrium of the following game is in the point (2,2).

(b) The Nash equilibrium of the following game is in the point (2,2).

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