Answer to Question #51663 in Microeconomics for Dipankar sonowal

Question

Find all the Nash equilibrium of the following game:
Player1
Player 2
Left Right
Up (5,4) (1,3)
Down (4,1) (2,2

Answer 1

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