Course outline
Module 1
Module 1: Introduction to Game Theory
Introduction to Game Theory
Knowledge check
Q1. What is game theory primarily concerned with?
- A. The study of computer algorithms
- B. The study of strategic decision making ✓
- C. The study of human psychology
- D. The study of economics only
Why: Game theory is focused on how individuals or entities make decisions in situations where the outcome depends on the actions of others.
Q2. Which of the following is a key assumption in game theory?
- A. Players act randomly
- B. Players have perfect information ✓
- C. Players always cooperate
- D. Players have unlimited resources
Why: Perfect information is a common assumption in many game theory models, though it is not always required.
Q3. What is a Nash equilibrium?
- A. A situation where all players are satisfied with their choices
- B. A situation where no player can benefit by changing their strategy while the others keep theirs unchanged ✓
- C. A situation where one player dominates the others
- D. A situation where all players lose
Why: A Nash equilibrium occurs when no player can benefit by changing their strategy if the others keep theirs unchanged.
Q4. What is a zero-sum game?
- A. A game where all players win
- B. A game where the total gains and losses of all players add up to zero ✓
- C. A game with no winner
- D. A game where all players lose
Why: In a zero-sum game, one player's gain is exactly balanced by another player's loss.
Q5. Which of the following is an example of a game theory scenario?
- A. A person reading a book
- B. A chess match between two players ✓
- C. A person walking in the park
- D. A person sleeping
Why: A chess match is a strategic interaction where each player's decision affects the outcome, making it a classic example of a game theory scenario.
Module 2
Module 2: Key Concepts and Terminology
Key Concepts and Terminology
Knowledge check
Q1. What is a situation in game theory where the outcome depends on the choices of two or more players?
- A. A game ✓
- B. A decision
- C. A strategy
- D. A move
Why: A game is a situation where the outcome depends on the choices of two or more players.
Q2. Which of the following is a key concept in game theory that refers to a player's plan of action?
- A. Outcome
- B. Payoff
- C. Strategy ✓
- D. Equilibrium
Why: A strategy is a key concept in game theory that refers to a player's plan of action.
Q3. What is the term used to describe a set of strategies where no player can benefit by changing their strategy while the other players keep theirs unchanged?
- A. Nash Equilibrium ✓
- B. Dominant Strategy
- C. Zero-Sum Game
- D. Pareto Efficiency
Why: Nash Equilibrium is the term used to describe a set of strategies where no player can benefit by changing their strategy while the other players keep theirs unchanged.
Q4. In a zero-sum game, what is the total sum of all players' payoffs?
- A. Zero ✓
- B. Positive
- C. Negative
- D. Undefined
Why: In a zero-sum game, the total sum of all players' payoffs is zero.
Q5. Which of the following refers to a strategy that yields the best outcome for a player regardless of the strategies chosen by others?
- A. Nash Equilibrium
- B. Dominant Strategy ✓
- C. Minimax Strategy
- D. Mixed Strategy
Why: A dominant strategy is a strategy that yields the best outcome for a player regardless of the strategies chosen by others.
Module 3
Module 3: Strategic Decision Making
Strategic Decision Making
Knowledge check
Q1. What is a dominant strategy in game theory?
- A. A strategy that leads to the worst outcome for the player
- B. A strategy that yields the best outcome for the player regardless of the opponent\'s choice ✓
- C. A strategy that depends on the opponent\'s move
- D. A strategy that is only useful in cooperative games
Why: A dominant strategy is one that provides the best outcome for a player no matter what the other player does.
Q2. In a zero-sum game, what is true?
- A. All players can benefit simultaneously
- B. The total gains and losses of all players sum to zero ✓
- C. There is no Nash equilibrium
- D. Players always cooperate
Why: In a zero-sum game, the total gains of one player equal the total losses of the other player.
Q3. What is a Nash equilibrium?
- A. A situation where all players are trying to change their strategy
- B. A situation where no player can benefit by changing their strategy while the others keep theirs unchanged ✓
- C. A strategy that always leads to the best possible outcome
- D. A strategy used only in non-cooperative games
Why: A Nash equilibrium occurs when no player has an incentive to deviate from their current strategy, given the strategies of others.
Q4. Which of the following is an example of a simultaneous move game?
- A. Chess
- B. Auctions
- C. Rock-Paper-Scissors ✓
- D. Negotiation between two companies
Why: Rock-Paper-Scissors is a simultaneous move game because both players choose their moves at the same time without knowing the other\'s choice.
Q5. What is a mixed strategy?
- A. A strategy where a player always chooses the same action
- B. A strategy where a player randomly chooses between different actions according to certain probabilities ✓
- C. A strategy used only in cooperative games
- D. A strategy that guarantees a win
Why: A mixed strategy involves randomizing between different actions to make it difficult for opponents to predict the player\'s move.
Module 4
Module 4: Nash Equilibrium Explained
Nash Equilibrium Explained
Knowledge check
Q1. What is a Nash Equilibrium?
- A. A situation where no player can benefit by changing their strategy while the other players keep theirs unchanged. ✓
- B. A situation where all players can benefit by changing their strategy.
- C. A situation where only one player can benefit by changing their strategy.
- D. A situation where players alternate strategies to maximize their gains.
Why: Because a Nash Equilibrium is defined as a stable state where no player has an incentive to deviate from their chosen strategy.
Q2. In a Nash Equilibrium, what is true about players' strategies?
- A. They are all cooperative.
- B. They are all non-cooperative.
- C. They are optimal given the strategies of others. ✓
- D. They are random and unpredictable.
Why: Because each player's strategy is optimal given the strategies of the other players.
Q3. Which of the following is a key assumption in Nash Equilibrium?
- A. Players act with complete uncertainty.
- B. Players act rationally and have perfect information. ✓
- C. Players act irrationally and have incomplete information.
- D. Players act randomly without any strategy.
Why: Because rationality and perfect information are essential for players to choose strategies that lead to Nash Equilibrium.
Q4. Which game is a classic example of Nash Equilibrium?
- A. Rock-Paper-Scissors
- B. Prisoner's Dilemma ✓
- C. Chess
- D. Monopoly
Why: Because the Prisoner's Dilemma clearly demonstrates a Nash Equilibrium where both players choose to defect.
Q5. What happens if a player deviates from a Nash Equilibrium strategy?
- A. They always gain more.
- B. They always lose.
- C. They do not gain any benefit. ✓
- D. They gain benefit only if others change strategies.
Why: Because in a Nash Equilibrium, no player can benefit by changing their strategy while others keep theirs unchanged.
Module 5
Module 5: Zero-Sum Games and Solutions
Zero-Sum Games and Solutions
Knowledge check
Q1. In a zero-sum game, what is the total sum of all players\' payoffs?
- A. Zero ✓
- B. Positive
- C. Negative
- D. Undefined
Why: In a zero-sum game, the total sum of all players\' payoffs is always zero because one player\'s gain is exactly balanced by another player\'s loss.
Q2. What is the primary goal of a player in a zero-sum game?
- A. Maximize their own payoff
- B. Minimize the opponent\'s payoff
- C. Both A and B ✓
- D. Ensure a draw
Why: In a zero-sum game, the primary goal of a player is to maximize their own payoff while minimizing the opponent\'s payoff, as the two objectives are equivalent in such games.
Q3. What is the solution concept most commonly used in zero-sum games?
- A. Nash Equilibrium ✓
- B. Dominant Strategy
- C. Maximin Strategy
- D. Pareto Efficiency
Why: The Nash Equilibrium is the most commonly used solution concept in zero-sum games because it identifies a stable outcome where no player can benefit by unilaterally changing their strategy.
Q4. In a zero-sum game, if one player has a dominant strategy, what can be said about the other player\'s strategies?
- A. They are also dominant
- B. They are not dominant
- C. They are irrelevant
- D. They are dominated ✓
Why: In a zero-sum game, if one player has a dominant strategy, the other player\'s strategies are typically dominated because the dominant strategy of the first player ensures a better outcome regardless of the second player\'s choice.
Q5. Which of the following is a characteristic of a zero-sum game?
- A. All players have the same payoff
- B. The sum of all payoffs is always zero ✓
- C. There are no pure strategy equilibria
- D. Players can communicate freely
Why: A defining characteristic of a zero-sum game is that the sum of all players\' payoffs is always zero, meaning one player\'s gain is exactly balanced by another\'s loss.
Module 6
Module 6: Non-Zero-Sum Games and Cooperation
Non-Zero-Sum Games and Cooperation
Module 7
Module 7: Applications in Real Life
Applications in Real Life
Knowledge check
Q1. What is a common real-life application of game theory in economics?
- A. Weather forecasting
- B. Auction design ✓
- C. Music composition
- D. Sports training
Why: Game theory is widely used in auction design to determine optimal bidding strategies and maximize revenue.
Q2. Which of the following is an example of a zero-sum game in real life?
- A. Negotiation between two companies
- B. A poker game between two players ✓
- C. A business partnership
- D. A public debate
Why: In a poker game, the total gains of one player equal the total losses of the other, making it a zero-sum game.
Q3. In which field is game theory used to model the interactions between countries during trade negotiations?
- A. Environmental science
- B. International relations ✓
- C. Culinary arts
- D. Fashion design
Why: Game theory is used in international relations to analyze and predict outcomes of trade negotiations and diplomatic interactions.
Q4. Which of the following scenarios best illustrates the prisoner's dilemma in real life?
- A. Two friends deciding on a movie to watch
- B. Two companies competing in a market
- C. Two suspects being interrogated separately ✓
- D. Two students collaborating on a project
Why: The prisoner's dilemma is best illustrated by two suspects being interrogated separately, where each has an incentive to betray the other, even though mutual cooperation would lead to a better outcome.
Q5. What is a key application of game theory in computer science?
- A. Designing user interfaces
- B. Creating algorithms for decision-making in AI ✓
- C. Writing poetry
- D. Developing music software
Why: Game theory is used in AI to create algorithms that make optimal decisions in competitive or uncertain environments.