Name

1. In a simple strategic form game we need to have four lists of information.  These lists are
a.
b.
c.
d.

2. When players move simultaneously we usually write the game in its  or  form.

3. When players move sequentially we usually write the game in its form.

4. Brock Lea and Ann Tchovie are planning the menu for their party.  They are doing the planning independently.  Their menu choices and payoffs can be represented in the form of a game.

a. Which outcome would Brock Lea most prefer?
  Asparagus and Hot Dogs Asparagus and Burgers Fries and Hot Dogs Fries and Burgers

b. Which outcome would Ann Tchovie most prefer?
 Asparagus and Hot Dogs Asparagus and Burgers Fries and Hot Dogs Fries and Burgers

c. Which outcome results in the greatest value to the players? (You can assume that payoffs are additive.)
 Asparagus and Hot Dogs Asparagus and Burgers Fries and Hot Dogs Fries and Burgers

d. Will Ann ever play her 'Hot Dog' strategy? Yes No

e. Will Brock ever play his Asparagus strategy? Yes No

5. There are two firms in an industry.  Each firm's gross revenue depends on its own advertising expenditure and the expenditure of its rival.  Specifically, total revenue for each firm is given by

TR₁ = (10-a₂)a₁ - a₁²

TR₂ = (10 - a₁)a₂ - a₂²

Notice that the gross revenue functions for the firms are symmetric.  Whatever we learn about firm 1 must also be true for firm 2.

a. If firm 2 spends $2 on advertising, how much should firm 1 spend in order to maximize its revenues?

b. If firm 2 spends $3 on advertising, how much should firm 1 spend in order to maximize its revenues?

c. If firm 2 spends $4 on advertising, how much should firm 1 spend in order to maximize its revenues?

d. What are the intercept and slope for firm 1's reaction function? (Hint: plot the points from a., b. and c., draw in the line and find the answer.) a₁ = + a₂.

e. What are the slope and intercept for firm 2's reaction function?
a₂ = + a₁.

f. Use your answer to d. and e. to find the advertising to be done by each firm.
a₁ =        a₂ =

6. Brock and Ann have food on their minds again.  They can go out to dinner or stay at home; Ann makes that decision.  If they stay home then Brock cooks either a Swanson TV dinner or a Lean Cuisine frozen entree.  The game tree looks like

a. Whose move is at the root of the tree? Brock Lea Ann Tchovie

b. At how many nodes does Brock have a strategic choice?

c. What choice will Brock make? Swanson Lean Cuisine

d. Given Brock's choice, what will Ann do? Out Home

e. Will Ann ever choose to go out to dinner? Yes  No

7. Miss Ann Thrope and Anne Droyd are locked in an epic struggle over the market for robots. They can each choose to advertise a little (Lo) or a lot (Hi).  Their payoffs are profits and the strategic game they are playing is shown below.

In the following questions the row player's (Droyd) strategy is listed first.

a. Which outcome has the greatest total value to the players?
     Lo, Lo  Lo, Hi  Hi, Lo  Hi, Hi

b. Which outcome is preferred by Thrope?
   Lo, Lo Lo, Hi  Hi, Lo  Hi, Hi

c. Which outcome is preferred by Droyd?
   Lo, Lo  Lo, Hi  Hi, Lo   Hi, Hi

d. Will Droyd ever play Lo?
   Yes    No

e.  Will Thrope ever play Lo?
    Yes   No

f. If they each play their preferred strategy, what are their payoffs?
Droyd =           Thrope = 

g. Does your answer in f. correspond with the strategic choices that maximize the value of the game?   Yes  No

h. Does the outcome in f. correspond to Droyd's preferred outome?  Yes  No  To Thrope's preferred outcome? Yes  No