Chapter 18: Game Theory and Oligopoly: Strategic Interactions in Macroeconomics

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Tailored notes based on your materials, expanded with key definitions, examples, and context.

Game Theory and Oligopoly

Introduction to Strategic Thinking

Strategic thinking is essential in situations where the outcome of your decision depends on the choices of others. In economics, this is especially relevant in markets with a few dominant firms (oligopoly), where each firm's actions affect the others.

Strategic interaction: Occurs when your best choice depends on what others choose, and their best choice depends on what you choose.
Both collaboration and competition involve strategic interactions.
Examples: Business pricing, political voting, and social decisions.

Game Theory: A Brief History

1920s–1940s: John von Neumann developed the mathematical foundation for zero-sum games (pure conflict, e.g., chess, warfare).
1950s: John Nash introduced the concept of Nash Equilibrium, extending game theory to all strategic situations.
1950s–1980s: Game theory applied to Cold War strategy (e.g., arms race, mutually assured destruction).
1980s–present: Game theory became a standard tool in economics, especially for analyzing markets with asymmetric information (e.g., auctions, bargaining, insurance, credit, and used car markets).

Four Steps for Making Good Strategic Decisions

Consider all possible outcomes: Use a payoff table (or matrix) to list all possible choices and their results.
Think about the "what ifs" separately: Analyze each possible scenario based on the other player's choices.
Play your best response: For each scenario, choose the action that yields the highest payoff for you.
Put yourself in other people's shoes: Predict what your rival will do by assuming they are also thinking strategically.

Payoff Tables and Matrices

A payoff matrix is a table that shows the outcomes (payoffs) for each combination of strategies by the players.

Each row represents one player's choices; each column represents the other's.
Each cell shows the payoffs for both players, often as ordered pairs (row player's payoff, column player's payoff).

Example Payoff Matrix

	Professor puts game theory on the exam	Professor omits game theory from the exam
You pay attention	Y: Ace the exam P: 😊	Y: Wasted time P: 😐
You tune out	Y: Fail the exam P: 😢	Y: Save time + good grade P: 😊

Best Response and Dominant Strategy

Best response: The action that yields the highest payoff for a player, given the other player's choice.
Dominant strategy: A strategy that is the best response to every possible choice of the rival.
Not all players have a dominant strategy in every game.

Nash Equilibrium

A Nash equilibrium occurs when each player's strategy is the best response to the other's strategy. No player can improve their payoff by changing their own choice alone.

In a Nash equilibrium, both players are doing the best they can, given the other's choice.
Checkmark method: Place a check next to each player's best response in the payoff matrix. A cell with checks from both players is a Nash equilibrium.

Example: Nash Equilibrium in Payoff Matrix

	Professor puts game theory on the exam	Professor omits game theory from the exam
You pay attention	Y: Ace the exam P: 😊	Y: Wasted time P: 😐
You tune out	Y: Fail the exam P: 😢	Y: Save time + good grade P: 😊

In this example, the Nash equilibrium is for you to pay attention and for the professor to put game theory on the exam.

Pure vs. Mixed Strategies

Pure strategy: Always choosing the same action.
Mixed strategy: Randomizing between actions to keep the opponent guessing.
Every game has at least one Nash equilibrium, but sometimes it requires mixed strategies.

The Prisoner's Dilemma

The Prisoner's Dilemma is a classic example of a game where rational players may fail to cooperate, even though cooperation would make them both better off.

Each player has a dominant strategy to "defect" (betray the other), leading to a worse outcome for both.
The dilemma illustrates why cooperation is hard to achieve in strategic settings.

Prisoner's Dilemma Payoff Matrix

	Clyde denies	Clyde confesses
Bonnie denies	Bonnie: 1 year Clyde: 1 year	Bonnie: 3 years Clyde: 0 years
Bonnie confesses	Bonnie: 0 years Clyde: 3 years	Bonnie: 2 years Clyde: 2 years

Real-World Applications: Oligopoly and the Prisoner's Dilemma

Oligopolies (markets with a few large firms) often face Prisoner's Dilemma situations, such as in advertising or price-fixing.
Example: Coke and Pepsi could both benefit by not advertising, but each has an incentive to advertise if the other does not.

Oligopoly Advertising Payoff Matrix

	Pepsi cooperates (no advertising)	Pepsi defects (advertises)
Coke cooperates (no advertising)	Coke: $2b Pepsi: $2b	Coke: $0b Pepsi: $3b
Coke defects (advertises)	Coke: $3b Pepsi: $0b	Coke: $1b Pepsi: $1b

The Nash equilibrium is for both to advertise, even though both would be better off cooperating and not advertising.

Coordination Games

Coordination games occur when players are better off if they coordinate their choices, but there may be multiple equilibria (good and bad outcomes).

Examples: Political revolutions, bank runs, macroeconomic booms and recessions.
Failure to coordinate can lead to suboptimal outcomes (e.g., recessions, bank runs).

Sequential Games and First/Second Mover Advantage

In sequential games, players make decisions one after another, and the order of moves matters.

First-mover advantage: The player who moves first can commit to a strategy that benefits them.
Second-mover advantage: The player who moves second can adapt to the first player's choice.
Game trees and backward induction are used to analyze sequential games.

Key Terms and Concepts

Payoff matrix: Table showing payoffs for each combination of strategies.
Best response: The optimal action given the other player's choice.
Dominant strategy: Best response to all possible choices of the rival.
Nash equilibrium: Set of strategies where no player can benefit by changing their own strategy alone.
Pure strategy: Always choosing the same action.
Mixed strategy: Randomizing between actions.
Coordination game: Game with multiple equilibria where players benefit from making the same choices.
Sequential game: Game where players move in sequence, not simultaneously.
Backward induction: Solving a sequential game by reasoning backward from the end.

Formulas and Notation

Payoff matrix notation: For a two-player game, the payoff matrix is often written as: where is the payoff to the row player and is the payoff to the column player.

Summary Table: Types of Games

Game Type	Key Feature	Example
Prisoner's Dilemma	Dominant strategy to defect; cooperation is better but unstable	Oligopoly advertising, price fixing
Coordination Game	Multiple equilibria; best if players coordinate	Bank runs, political revolutions
Sequential Game	Order of moves matters; analyzed with backward induction	Entry deterrence, first/second mover advantage

Additional info: These notes expand on the slides by providing definitions, examples, and context for each concept, ensuring a self-contained study guide for macroeconomics students.