Suppose that two players are playing the following game Play

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 2 Left 6 1 94 Right Player 1 Top Bottom 24 53 ron the right is the payoff Player 2. A) (2 points) Does Player 1 have a dominant strategy, and if so what is it? B) (2 points) Does Player 2 have a dominant strategy and if so what is it? C) (1 point each) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not: ) Top/Left ii) Top/Right ili) Bottom/Left iv) Bottom Right D) (2 points) What is Player 1\'s maximin strategy? E) (2 points) What is Player 2\'s maximin strategy? F)(2 points If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?

Solution

A) When Player 2 takes Left , 1 will select : Top . When 2 takes Right , 1 will select : Top . So yes Player 1 has a dominant strategy and it is TOP .

B) When Player 1 takes Top 2 will play : Right . And when 1 palys Bottom , 2 will play : Left . So player 2 does not have any dominant strategy .

C) Nash Equilibrium : Top , Right = ( 9 , 4 )

D) When Player 1 plays Top , 2\'s payoff minimzing action against 1 is to play Left , yeilding 1 a payoff of 6 which is less than 9 .

When Player 1 plays bottom , 2\'s payoff minimizing action against 1 is to play Left , yeilding 1 a payoff of 2 which is less than 5 .

So , player 1 will play Top since that will yeild maximum of these two payoffs ( 6>2) .

So TOP is the maximin strategy for player 1 .