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# payoffs for an advertising game between Coke and Pepsi

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A monopolist has demand and cost curves given by:
QD = 10,000 - 20P
TC = 1,000 + 10Q + .05Q2

a. Find the monopolist's profit-maximizing quantity and price.
b. Find the monopolist's profit.

The following matrix shows the payoffs for an advertising game between Coke and Pepsi. The firms can choose to advertise or to not advertise. Numbers in the matrix represent profits; the first number in each cell is the payoff to Coke. (Numbers in millions.)

Don't Advertise (-50, 500) (100, 100)

a. Explain why this would be described as a Prisoner's Dilemma game.
b. Explain the probable outcome of this game.

#### Solution Preview

Question 1
a. First, let's write the demand functions as a function of Q:

Q = 10000 - 20P
P = - Q/20 + 10000/20 = -Q/20+ 500

Now, we have that total revenue for the monopolist is PQ (price times quantity sold), and the total cost is given by the TC function. Therefore, total profits are:

Profit = PQ - 1,000 - 10Q - .05Q^2

Replacing P with the one we found in the demand function:

Profit = (-Q/20+ 500)Q - 1,000 - 10Q - .05Q^2
Profit = -(Q^2)/20+ 500Q - 1,000 - 10Q - .05Q^2

Now we want to maximize profits. The usual procedure for doing this is to find the derivative of the profits function with ...

#### Solution Summary

Prisoner's Dilemma is depicted in this case. A payoff matrix is given for an advertising game between Coke and Pepsi.

\$2.19

## Nash Equilibrium: Coke and Pepsi Advertising Strategy

1. Find the solution to the following advertising decision game between Coke and Pepsi, assuming the firms act independently.

Pepsi's budget
Low Medium High

Low 400; 400 320; 720 560; 600
Coke's
budget Medium 500; 300 450; 525 540; 500

High 375; 420 300; 378 525; 750

Questions:
1.
a. Does Coke have a dominant strategy? If yes, what is it?
b. Does Pepsi have a dominant strategy? If yes, what is it?
c. What is the likely outcome of this advertising decision problem? Verify that your answer is a Nash equilibrium by explaining why it is strategically stable.
d. Pepsi's highest payoff occurs when Coke and Pepsi both choose high ad budgets. Explain why Pepsi will not likely choose a high ad budget.
2. What is tacit collusion? How would the behavior of the firms differ from that of members of a cartel? Why would tacit collusion exist?

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