Mixed Strategy Practice Problems

Name 

 

1. Lex E. Kahn and Thea Sorus are publishers. Lex can either expand or hold constant the number of authors he has under contract. Thea can either publisher her lead author's new book in electronic format or publish it in the standard paper format. The payoff matrix, in thousands of dollars of profit, for the two publishers is shown below.

   

Lex E. Kahn
   

Expand

Hold

Thea Sorus

Paper

0, 3

3, 0

Electronic

2, 1

1, 2

  1. Does this game have any dominant strategies?
    Yes No No
  2. Are there any dominated strategies?
    Yes No No
  3. Are there any pure strategy Nash equilibria? (Hint: Find Lex's and Thea's best response plays.)
    Yes No No
  4. Let p be the probability that Lex expands and q be the probability that Thea goes electronic. Find the values for p and q in Lex's and Thea's mixed strategies.
    P= =1/2  Q= =3/4
  5. Are the mixed strategies a Nash equilibrium?
    Yes No
    Yes
     How do you know?

    Each mixed strategy has been constructed as a best response to the opponent's play.
  1. Phil A. Mignon and Sal Monella are restaurateurs in Philadelphia. On the occasion of the 2000 Republican National Convention both are contemplating mounting special promotions.
   

Sal Monella
   

No Promo

Promotion

Phil A. Mignon

No Promo

3, 1

0, 0

Promotion

0, 0

1, 4
  1. Find the pure strategy Nash equilibria of the game.
    {Promo, Promo} and {No Pro, No Pro}
  2. Find the mixed strategies for Phil and Sal.

    Phil A. Mignon probability of Promo 1/5
    Sal Monella probability of Promo 3/4