Welcome to the World of Strategy!
In our previous chapters, we looked at firms that either had no power (Perfect Competition) or total power (Monopoly). But what happens when a few giant firms have to share the market? This is an Oligopoly, and things get very interesting here because firms have to play "mind games" with each other. This chapter introduces Game Theory, the mathematical tool economists use to predict how these firms will behave.
1. The Core of Oligopoly: Interdependence
The most important thing to remember about an Oligopoly is interdependence. This means that the profit of one firm depends not just on its own actions, but also on the actions of its competitors.
Analogy: Imagine you and a friend are selling lemonade on the same street. If you lower your price, your friend loses customers. If your friend starts a massive advertising campaign, you might lose customers. You are "interdependent" because your success depends on what the other person does.
2. Introduction to Game Theory
Game Theory is the study of how people or firms behave in strategic situations. To analyze a "game" in AP Microeconomics, we look at three things:
- Players: The firms involved (usually two firms in AP problems).
- Strategies: The choices available to the firms (e.g., "High Price" or "Low Price").
- Payoffs: The outcomes for each firm, usually measured in profit (\$).
The Payoff Matrix
We represent these games using a Payoff Matrix. It’s a table that shows every possible combination of strategies and the resulting profits.
Important Convention: In a standard matrix, the first number in each box belongs to the player on the Left (the Row player), and the second number belongs to the player on the Top (the Column player).
3. Dominant Strategy
A Dominant Strategy is a strategy that is the best choice for a player no matter what the other player does.
How to find a Dominant Strategy (Step-by-Step):
Don't worry if this feels like a puzzle at first! Follow these steps for "Firm A" (on the left):
1. Assume Firm B chooses "Strategy 1." Which choice gives Firm A a higher payoff? (Circle it).
2. Assume Firm B chooses "Strategy 2." Which choice gives Firm A a higher payoff? (Circle it).
3. Check: If Firm A chose the same strategy in both scenarios, that is their Dominant Strategy.
Note: A firm might not have a dominant strategy! If their best choice depends on what the other firm does, they do not have one.
4. Nash Equilibrium
A Nash Equilibrium is an outcome where neither player has an incentive to deviate (change their mind) unilaterally. In other words, given what the other player is doing, neither player would want to change their own action.
Quick Tip: In a payoff matrix, a Nash Equilibrium is any box where both numbers are the best possible results for the players given the other's choice. If you used the "circle the best payoff" method from above for both players, the box with two circles is the Nash Equilibrium.
Key Takeaway: Every game has at least one Nash Equilibrium, but not every player has a dominant strategy.
5. The Prisoner’s Dilemma
The Prisoner's Dilemma is a specific type of game that explains why it is so hard for oligopolies to cooperate. It has two main features:
- Both players have a dominant strategy.
- When both players follow their dominant strategy, they end up with a worse payoff than if they had cooperated.
Example: Two firms could both charge a "High Price" and earn \( \$100 \) each. However, if Firm A cheats and lowers its price, it could earn \( \$150 \) while Firm B earns \( \$20 \). Because both firms have an incentive to cheat (to get that \( \$150 \)), they both end up charging a "Low Price" and earning only \( \$50 \) each.
Collusion: This is when firms agree to cooperate (like both picking "High Price"). However, as the Prisoner's Dilemma shows, there is always an incentive to cheat on the agreement to try and capture more profit.
6. Incentives to Alter Actions
The AP exam often asks what would happen if the payoffs changed. For example, if the government provides a subsidy for a specific action or if a new tax is implemented.
How to handle this:
1. Change the numbers in the matrix based on the new information (e.g., add the subsidy amount to the payoff).
2. Re-run your "circle the best payoff" test.
3. See if the Dominant Strategy or Nash Equilibrium shifts to a new box.
Quick Review Box:
• Interdependence: My profit depends on your move.
• Dominant Strategy: My best move regardless of your move.
• Nash Equilibrium: The "stable" outcome where no one wants to change.
• Prisoner's Dilemma: Following self-interest leads to a worse outcome for everyone.
Common Pitfalls to Avoid
• Mixing up the players: Always double-check which number belongs to which firm. Remember: (Left Player, Top Player).
• Assuming there is always a dominant strategy: Sometimes a firm’s best move depends entirely on the other firm. If they choose "Up" when you go "Left" but "Down" when you go "Right," they don't have a dominant strategy.
• Forgetting "Unilateral": In a Nash Equilibrium, we only care if one person wants to move at a time. We don't ask "would they both want to move together?"
Final encouraging thought: Game theory is just a formal way of playing "If they do this, I'll do that." Once you master the "circle the highest number" trick, you'll find these questions are some of the most consistent points you can earn on the exam!