Part 1:

These question builds off the Section 3 Lesson, Practice Problem 2. They are to ensure you understand key technical definitions before advancing to part 2.

Entrant (payoffs on right)

Enter Don’t enter

Monopolist (payoffs on left) Price High 20 10 50 0

Price Low 5 -10 10 0

This is a simultaneous choice, non-cooperative game.

There are four possible outcomes:

Outcome 1: Monopolist Prices High, Entrant Enters

Outcome 2: Monopolist Prices Low, Entrant Enters

Outcome 3: Monopolist Prices High, Entrant Doesn’t Enter

Outcome 4: Monopolist Prices Low, Entrant Doesn’t Enter

1. Referencing the payoffs above and the textbook definition of dominant strategy:

a. Explain why the monopolist has a dominant strategy to price high.

b. Explain why the entrant does not have a dominant strategy.

2. Which outcome has the highest payoff for:

a. The entrant?

b. The monopolist?

An alternative (but equivalent) definition of Nash equilibrium to the formal version in the textbook is: “an outcome (e.g. one of those above), in which no player (e.g. the monopolist and the entrant) can be made better off by unilaterally changing their strategy.”

3. Using the textbook definition or the alternative above, explain why the Nash equilibrium in this case is Outcome 1 (Monopolist Prices High, Entrant Enters).

4. The above payoffs have an underlying economic story. Thinking about the economics of market structure you’ve learned in this class, give a potential justification for why:

a. The monopolist’s payoffs are always lower when the entrant enters.

b. The entrant’s payoffs are negative in Outcome 2 (Monopolist Prices Low, Entrant Enters).

Part 2:

Consider a simple 2 x 2 game theory matrix such as this one:

Player 2 (P2)

Action 3

Action 4

Player 1 (P1) Action 1

Payoff (P1) Payoff (P2) Payoff (P1) Payoff (P2)

Action 2

Payoff (P1) Payoff (P2) Payoff (P1) Payoff (P2)

1. Make up your own simultaneous move, non-cooperative game theory example that you think can be distilled into this framework. The example can come from your own experience in a business environment OR you can choose a local business and analyze a hypothetical game theoretic situation they might face.

Put two players and four actions in the table below (recall that depending on the context, actions 3 and 4 could be the same as actions 1 and 2):

2. Finish the table with a numerical payoff structure that makes sense. Remember that the specific numbers that you choose matter less than how the payoffs from different actions differ from each other. Make sure that each outcome makes economic sense relative to the other outcomes!

3. Describe your reasoning behind the payoffs from each outcome. Make sure you explain each square.

4. Does either player have a dominant strategy? If so, what?

5. What are the Nash equilibria, if any?

6. Reflect on your example: do you think the game theory tools above help you predict the real-world outcome? What things are missing? How could you change your example to better match the real world? Be specific!