Question

3. For each of the following statements, say whether it is true or false, and explain your answer. (a) "A roll-back equilibrium is not a Nash equilibrium.. (b) "If a simultaneous-move game has pure strategy equilibria, the game cannot have mixed strategy equilibria too." (c) "Players who have a strictly dominant pure strategy will never choose to play a mixed strategy."

Answer 1

Answer:

A) A roll – back equilibrium is not a Nash equilibrium: false

Because a roll – back equilibrium is a Nash equilibrium. Roll back method is used for sequential games the optimal strategy of all players are determined by moving backward and the Nash equilibrium of sub game is determined. But a Nash equilibrium is not necessarily a roll – back equilibrium

B) if a simultaneous – move game has pure strategy equilibria the game cannot have mixed strategy quilibria too: true

because in simultaneous move game player has only one Nash equilibrium it can be either pure strategy Nash equilibrium or mixed strategy Nash equilibrium

C) Players who have a strictly dominant pure strategy will never choose to play a mixed strategy: True

Because a dominant strategy will give player higher payoff regardless of the strategies of his opponent so player will always prefer strictly dominant strategy