9781118041581

dealer has available, the better is its chance of making a sale. In fact, a

particular dealer’s share of the total market is proportional to the

number of cars it holds in its showroom. Thus, dealer 1’s profit can be

expressed as  1 3,200,000[x 1 /(x 1 x 2 x 3 x 4 )] 2,400x 1. The

profit expressions for the other dealers are analogous.

The partial spreadsheet that follows lists the profit of a typical dealer

(for various inventories) when it faces competitors with different average

inventories. For instance, if dealer 1 stocks an inventory of 250 cars when

the other dealers do likewise, then dealer 1’s inventory is 25 percent of

the total. Thus, it sells exactly (.25)(800) 200 cars at a price of $4,000

each, while paying for 250 cars at $2,400 each. Its net profit is $200,000.

a. Create a spreadsheet to complete the entries in the following payoff

table. (Hint: To compute cell G10, enter the formula:

Then simply copy this formula into the other cells of the table.) Adding

dollar signs creates the appropriate absolute references to the dealers’

inventory levels. For the row player’s action, the sign always goes before

the alphabetical coordinate, $B10. For the column player’s action, it

goes before the numerical reference, G$5. Also, in cells D7-D10 and E7,

dealer 1 sells its entire inventory; thus, its payoffs are computed

accordingly.)

 3200 $B10/($B10 3 G$5)2.4*$B10.

436 Chapter 10 Game Theory and Competitive Strategy

ABCD E F G H I JK

1

2 USED CAR DEALERS

3

4 Dealer 1’s Average Auto Inventory of the Other Three Dealers

5 Inventory 175 200 225 250 275 300 325

6

7 175 280.0 280.0 238.8 185.4

8 200 320.0 320.0 251.4 193.7

9 225 360.0 332.7 260.0 198.5

10 250 400.0 341.2 264.9 200.0

11 275

12 300

13 325

14 350

15

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