Name

1. Let's Make a Deal Barbara Seville is a documentary film maker trying to strike a deal with Cora Morant, a leading actress and amateur orntihologist, for the production of a film.  They estimate the film is capable of making $100,000 in profits.  The offer on the table is that they split the profits evenly.  If they both agree then the film is made.  If either one of them rejects the deal then no film is made and there is no money for either of them.  The normal form of the game is

Define an equilibrium as a pair of strategies such that neither player would change her strategy given the choice of the opponent.  

a. How many equilibria are there in the game?

b. Is the game dominance solvable? Yes  No

c. How many solutions are there in the game?

d. Are all of the equilibria also solutions? Yes   No

2. Advertising Two firms must make advertising decisions.  The amount spent by each firm on its advertising is x_i for i = 1 and 2.  Firm 1's profits are represented by π₁(x₁,x₂) = 1000x₁-x₁²-x₂² .

a. How much should firm 1 spend on advertising, treating firm 2's spending as a constant?

b. Firm 2's profits are given by π₂(x₁,x₂) = 1000x₂-x₁x₂-x₂² .  How much should firm 2 spend on advertising?

c. Suppose that Warren Peace purchases both firms.  He now makes the advertising decision to maximize the joint profits of his two subsidiaries.  How much should each subsidiary spend in order to maximize combined profits? Firm 1 = Firm 2 =

3. Nash Equilibrium Exam the following two person, normal form game:

a. Does Player 1 have a strictly dominant strategy? Yes No

b. Does Player 2 have a strictly dominant strategy? Yes  No

c. Does Player 1 have any weakly dominated strategies? Yes  No

d. Does Player 2 have any weakly dominated strategies? Yes  No

e. What is Player 1's best response to a play of Z by Player 2?

f. How many Nash equilibria are there in this game?

g. What are they? Remember that 1's strategy always is written first.  Check all that apply.

 J, X    J, Y    J, Z

 K, X   K, Y    K, Z

 L, X    L, Y    L, Z

 M, X   M, Y   M, Z

h. Is there an iterative elimination of dominated strategies solution to this game?  If so, enter your answer below; Player 1's strategy first.