Course outline
Module 1
Module 1: Introduction to Game Theory
Introduction to Game Theory
Knowledge check
Q1. What is the primary focus of game theory?
- A. To analyze the behavior of individuals in isolation
- B. To study strategic interactions between rational decision-makers ✓
- C. To predict the weather patterns in different regions
- D. To understand the flow of electricity in circuits
Why: Game theory focuses on strategic decision-making among rational agents where the outcome for each depends on the actions of others.
Q2. Which of the following is a key assumption in game theory?
- A. Players act irrationally and without any strategy
- B. Players have complete information about the game and other players' strategies ✓
- C. Players always make decisions based on emotions
- D. Players do not consider the outcomes of their actions
Why: A key assumption in game theory is that players have complete information about the game and other players' strategies, although this can vary in different types of games.
Q3. What is a 'payoff' in game theory?
- A. A random event that affects the outcome of the game
- B. The result or benefit a player receives from a particular outcome ✓
- C. A rule that restricts the actions of a player
- D. A strategy that guarantees a win for all players
Why: A payoff in game theory refers to the result or benefit a player receives from a particular outcome of the game.
Q4. Which of the following is an example of a zero-sum game?
- A. A game of chess between two players ✓
- B. A cooperative business partnership
- C. A game of poker with multiple players
- D. A negotiation between two countries
Why: A zero-sum game is one where the total gains of one player equal the total losses of the other player. Chess is a classic example of a zero-sum game.
Q5. What is a dominant strategy in game theory?
- A. A strategy that leads to the worst possible outcome for the player
- B. A strategy that is the best regardless of what the other players do ✓
- C. A strategy that depends on the actions of other players
- D. A strategy that is only used in cooperative games
Why: A dominant strategy is one that provides the best outcome for a player regardless of the strategies chosen by other players.
Module 2
Module 2: Strategic Decision Making
Strategic Decision Making
Module 3
Module 3: Nash Equilibrium
Nash Equilibrium
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 are trying to maximize their own payoffs regardless of others.
- C. A situation where one player has a dominant strategy and others have no strategy.
- D. A situation where players cooperate to achieve the best possible outcome for all.
Why: A Nash Equilibrium occurs when no player can benefit by changing their strategy while the other players keep theirs unchanged.
Q2. In a Nash Equilibrium, what is true about the players' strategies?
- A. They are all the same.
- B. They are all independent.
- C. They are all optimal given the strategies of others. ✓
- D. They are all random.
Why: In a Nash Equilibrium, each player's strategy is optimal given the strategies of the other players.
Q3. Which of the following is a key assumption in the definition of Nash Equilibrium?
- A. Players are rational and have complete information. ✓
- B. Players are irrational and act randomly.
- C. Players do not know their own payoffs.
- D. Players always cooperate with each other.
Why: A key assumption in Nash Equilibrium is that players are rational and have complete information.
Q4. In a game with two players, if both players are playing their best responses to each other, what can be said about the game?
- A. It is in a Nash Equilibrium. ✓
- B. It is in a Pareto optimal outcome.
- C. It is in a dominant strategy equilibrium.
- D. It is in a zero-sum game.
Why: If both players are playing their best responses to each other, the game is in a Nash Equilibrium.
Q5. Which of the following is NOT a requirement for a Nash Equilibrium?
- A. Players must have complete information.
- B. Players must have a dominant strategy. ✓
- C. Players must be rational.
- D. Players must be making decisions simultaneously.
Why: A Nash Equilibrium does not require that players have a dominant strategy; it only requires that each player's strategy is optimal given the strategies of others.
Module 4
Module 4: Zero-Sum Games
Zero-Sum Games
Knowledge check
Q1. In a zero-sum game, what is the total sum of all players' payoffs?
- A. Zero ✓
- B. Positive
- C. Negative
- D. Variable
Why: In a zero-sum game, the total sum of all players' payoffs is always zero, as one player's gain is exactly balanced by another's loss.
Q2. Which of the following is a characteristic of a zero-sum game?
- A. All players can win simultaneously
- B. One player's gain is another player's loss ✓
- C. There are no losses for any player
- D. The game always ends in a draw
Why: In a zero-sum game, one player's gain is exactly balanced by another player's loss.
Q3. What is the primary goal of a player in a zero-sum game?
- A. Maximize their own payoff
- B. Minimize their own loss
- C. Maximize the opponent's loss
- D. All of the above ✓
Why: In a zero-sum game, the primary goal of a player is to maximize their own payoff, which is equivalent to minimizing their own loss or maximizing the opponent's loss.
Q4. What is the name of the strategy used to find the optimal solution in a zero-sum game with pure strategies?
- A. Dominant strategy
- B. Nash equilibrium
- C. Minimax strategy ✓
- D. Mixed strategy
Why: The minimax strategy is used to find the optimal solution in a zero-sum game with pure strategies, where each player tries to minimize their maximum possible loss.
Q5. In a zero-sum game, what does the term 'saddle point' refer to?
- A. A point where the game ends in a draw
- B. A point where the maximin and minimax values are equal ✓
- C. A point where all players have equal payoffs
- D. A point where no player can improve their payoff
Why: A saddle point in a zero-sum game refers to a point where the maximin and minimax values are equal, indicating an optimal solution in pure strategies.
Module 5
Module 5: Non-Zero-Sum Games
Non-Zero-Sum Games
Knowledge check
Q1. In a non-zero-sum game, what is true about the total payoff for all players?
- A. It is always zero
- B. It can be positive, negative, or zero ✓
- C. It is always positive
- D. It is always negative
Why: In non-zero-sum games, the total payoff for all players does not have to be zero; it can vary depending on the strategies chosen.
Q2. Which of the following is a characteristic of a non-zero-sum game?
- A. Players' interests are completely opposed
- B. There is no possibility of cooperation
- C. Players can benefit from cooperation ✓
- D. The game must have a single Nash equilibrium
Why: In non-zero-sum games, players can often benefit from cooperation, as their payoffs are not necessarily conflicting.
Q3. What is a Nash equilibrium in the context of non-zero-sum games?
- A. A situation where no player can benefit by changing their strategy while others keep theirs unchanged ✓
- B. A strategy that always leads to the highest payoff for one player
- C. A situation where all players choose the same strategy
- D. A strategy that guarantees a win for all players
Why: A Nash equilibrium is a stable state where no player can improve their outcome by unilaterally changing their strategy.
Q4. Which of the following is an example of a non-zero-sum game?
- A. Rock-Paper-Scissors
- B. Prisoner's Dilemma ✓
- C. Matching Pennies
- D. A game of chess
Why: The Prisoner's Dilemma is a classic example of a non-zero-sum game where cooperation can lead to better outcomes for both players.
Q5. In non-zero-sum games, what is the primary focus of analysis?
- A. Finding the dominant strategy for one player
- B. Maximizing individual payoff regardless of others
- C. Understanding the interactions between players and potential outcomes ✓
- D. Ensuring all players receive equal payoffs
Why: The primary focus in non-zero-sum games is on analyzing how players interact and how different strategies lead to various outcomes.
Module 6
Module 6: Repeated Games
Repeated Games
Knowledge check
Q1. What is a repeated game in game theory?
- A. A game played only once with no future interactions
- B. A game played multiple times with the same players ✓
- C. A game with only one player
- D. A game with no defined rules
Why: Repeated games involve multiple rounds of play between the same players, allowing for strategies that take into account past interactions.
Q2. Which of the following is a key feature of repeated games?
- A. Players cannot communicate
- B. Players can use strategies based on past actions ✓
- C. There is no possibility of cooperation
- D. The game always ends on the first round
Why: In repeated games, players can use strategies based on past actions, which can lead to cooperation and different outcomes compared to one-shot games.
Q3. What is the 'Folk Theorem' in the context of repeated games?
- A. A theorem that states all Nash equilibria are efficient
- B. A theorem that describes the set of possible equilibrium outcomes in repeated games ✓
- C. A theorem that guarantees perfect information in all games
- D. A theorem that states players cannot cooperate in repeated games
Why: The Folk Theorem states that in repeated games, any feasible and individually rational outcome can be sustained as a Nash equilibrium.
Q4. In a repeated game, what is a 'trigger strategy'?
- A. A strategy that increases payoffs every round
- B. A strategy that punishes a player for deviating from cooperation ✓
- C. A strategy that always chooses the same action regardless of history
- D. A strategy that ignores past actions and plays randomly
Why: A trigger strategy involves punishing a player for deviating from a cooperative path, often used to enforce cooperation in repeated games.
Q5. What is the main difference between a one-shot game and a repeated game?
- A. One-shot games have more players
- B. Repeated games involve multiple rounds of play ✓
- C. One-shot games have no payoffs
- D. Repeated games cannot have Nash equilibria
Why: The main difference is that repeated games are played over multiple rounds, allowing players to consider future interactions and adjust strategies accordingly.
Module 7
Module 7: Applications of Game Theory
Applications of Game Theory
Knowledge check
Q1. What is a Nash equilibrium?
- A. A situation where all players are worse off
- B. A situation where no player can benefit by changing their strategy while the other players keep theirs unchanged ✓
- C. A situation where only one player benefits
- D. A situation where all players have the same strategy
Why: Because a Nash equilibrium is defined as a stable state where no player can gain by unilaterally changing their strategy.
Q2. Which of the following is an example of a zero-sum game?
- A. Chess
- B. Rock-paper-scissors
- C. Prisoner's Dilemma
- D. Both A and B ✓
Why: Because in both chess and rock-paper-scissors, the total gains and losses of all players sum to zero.
Q3. In the prisoner's dilemma, what is the dominant strategy for both players?
- A. Cooperate
- B. Defect ✓
- C. Randomly choose
- D. Wait for the other player to decide
Why: Because defecting yields a better outcome for an individual regardless of the other player's choice.
Q4. What does the term 'dominant strategy' mean?
- A. A strategy that is always the worst choice
- B. A strategy that is always the best choice regardless of what others do ✓
- C. A strategy that depends on others' choices
- D. A strategy that is only used in cooperative games
Why: Because a dominant strategy is one that provides the best outcome for a player regardless of the strategies chosen by others.
Q5. Which of the following is a key assumption in game theory?
- A. Players act irrationally
- B. Players have perfect information ✓
- C. Players always cooperate
- D. Players have limited knowledge
Why: Because game theory often assumes that players have perfect information to make optimal decisions.