3 Consider the game below 1 P1s strategy Middle can never be

3. Consider the game below (1) P1\'s strategy \"Middle\" can never be a best response. True or False? Show why. Your mark depends on your explanation (2) P1\'s strategy \"Middle\" is a dominated strategy. True or False? Show why. Your mark depends on your explanation. Player 2 Left Right Player Top 1,3 Top 1,365 Middle 5,1 5,2 Bottom 9, 0,0

Solution

(1) In case of Player 2 playing Left the best response of Player 1 is to play Bottom as this gives a payoff of 9>5>1. If Player 2 plays Right, Player1\'s best response is to play Top as this is where Player 1 gets largest payoffs as 6>5>0. Thus iddle is never a best response for Player 1. This statement is thus true. iddle is never a best response for Player 1. Player 1 can always do better by choosing some other strategy.

(2) This is False. Neither of the other strategies for Player 1 dominates iddle. This is as if Player 1 plays Top then we have 1<5 and 6>5. Also if he plays Bottom we have 9>5 and 0<5. Thus Bottom also does not dominate iddle. iddle is thus not a dominated strategy.