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 study the behavior of individuals in isolation
- B. To analyze strategic interactions among rational decision-makers ✓
- C. To predict the outcomes of random events
- D. To model economic markets only
Why: Game Theory primarily focuses on strategic interactions among rational decision-makers, where the outcome for each participant depends on the actions of others.
Q2. In a game, what is a 'strategy'?
- A. A random event that affects the outcome
- B. A set of rules that govern the game
- C. A plan of action a player can take ✓
- D. A method of calculating payoffs
Why: A strategy is a plan of action a player can take in a game, depending on the situation and the actions of other players.
Q3. Which of the following is an example of a zero-sum game?
- A. Chess ✓
- B. Rock-Paper-Scissors
- C. Monopoly
- D. Poker
Why: Chess is a zero-sum game because one player's gain is exactly balanced by another player's loss.
Q4. What is a 'dominant strategy'?
- A. A strategy that yields the highest payoff regardless of the opponent's choice ✓
- B. A strategy that is chosen only when the opponent plays a specific strategy
- C. A strategy that leads to a Nash equilibrium
- D. A strategy that is never used in a game
Why: A dominant strategy is one that yields the highest payoff regardless of what the opponent does.
Q5. What is a Nash equilibrium?
- A. A situation where all players are choosing their best strategy given the strategies of others ✓
- B. A strategy that guarantees a win for one player
- C. A strategy that is used only in cooperative games
- D. A method of calculating expected payoffs
Why: A Nash equilibrium is a situation where all players are choosing their best strategy given the strategies of others, and no player has an incentive to deviate.
Module 2
Module 2: Strategic Form Games
Strategic Form Games
Knowledge check
Q1. In a strategic form game, what does each player's strategy set represent?
- A. The set of possible outcomes
- B. The set of actions a player can take ✓
- C. The set of payoffs received
- D. The set of opponents in the game
Why: A player's strategy set consists of all possible actions they can take in the game.
Q2. What is a dominant strategy?
- A. A strategy that is always the best response regardless of the opponent's strategy ✓
- B. A strategy that is never the best response
- C. A strategy that leads to a Pareto efficient outcome
- D. A strategy that is chosen only when the opponent chooses a specific strategy
Why: A dominant strategy is one that yields a higher payoff than any other strategy, regardless of what the other player does.
Q3. In a zero-sum game, what is the relationship between the players' payoffs?
- A. The sum of the payoffs is always zero ✓
- B. The sum of the payoffs is always positive
- C. The sum of the payoffs is always negative
- D. The sum of the payoffs depends on the strategies chosen
Why: In a zero-sum game, the total payoff for all players combined is always zero.
Q4. 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 maximizing their payoffs
- C. A situation where all players are using a dominant strategy
- D. A situation where the sum of payoffs is maximized
Why: A Nash equilibrium occurs when each player's strategy is the best response to the strategies of the other players.
Q5. What is a mixed strategy?
- A. A strategy where a player chooses a single action with certainty
- B. A strategy where a player randomly selects actions according to a probability distribution ✓
- C. A strategy that is always better than a pure strategy
- D. A strategy that is used only in cooperative games
Why: A mixed strategy involves a player randomly choosing between different actions according to a probability distribution.
Module 3
Module 3: Nash Equilibrium Concepts
Nash Equilibrium Concepts
Module 4
Module 4: Mixed Strategies and Equilibrium
Mixed Strategies and Equilibrium
Knowledge check
Q1. What is a mixed strategy in game theory?
- A. A strategy where a player chooses the same action every time
- B. A strategy where a player randomly selects actions according to a probability distribution ✓
- C. A strategy that guarantees the highest possible payoff
- D. A strategy that is always the best response to other players' strategies
Why: A mixed strategy involves randomizing between different actions to make the opponent's prediction difficult.
Q2. In a mixed strategy Nash equilibrium, what is true about players' strategies?
- A. All players use pure strategies
- B. Players' strategies are best responses to each other ✓
- C. Players always choose the same action
- D. No player can benefit by changing their strategy unilaterally
Why: In a Nash equilibrium, each player's strategy is a best response to the strategies of the other players.
Q3. Which of the following is a key requirement for a mixed strategy Nash equilibrium?
- A. All players have identical strategies
- B. Players randomize their strategies in a way that makes the other player indifferent between their pure strategies ✓
- C. Players always use the same probability distribution
- D. Players do not use any randomization
Why: For a mixed strategy to be part of a Nash equilibrium, it must make the opponent indifferent between their pure strategies.
Q4. What is the primary purpose of using mixed strategies in game theory?
- A. To ensure that all players receive the same payoff
- B. To avoid being exploited by opponents who predict your actions ✓
- C. To simplify the game for all players
- D. To guarantee a win in every scenario
Why: Using mixed strategies helps prevent opponents from predicting your actions, which can lead to better outcomes.
Q5. In a zero-sum game, what does a mixed strategy Nash equilibrium ensure?
- A. Both players receive the same payoff
- B. The expected payoff is maximized for both players
- C. The expected payoff is minimized for both players
- D. The expected payoff is maximized for one player and minimized for the other ✓
Why: In zero-sum games, the mixed strategy Nash equilibrium ensures that one player's expected maximum payoff is equal to the other's expected minimum payoff.
Module 5
Module 5: Zero-Sum Games and Minimax Theorem
Zero-Sum Games and Minimax Theorem
Module 6
Module 6: Extensive Form Games
Extensive Form Games
Knowledge check
Q1. In an extensive form game, what does a node represent?
- A. A player's strategy
- B. A point in the game where a player makes a decision ✓
- C. The outcome of the game
- D. A payoff to a player
Why: A node represents a decision point for a player in the game tree.
Q2. What is the term for a game that is represented as a tree with nodes and branches?
- A. Normal form game
- B. Extensive form game ✓
- C. Simultaneous game
- D. Repeated game
Why: An extensive form game is represented as a tree with nodes and branches showing the sequence of moves.
Q3. Which of the following is a characteristic of a perfect information game?
- A. Players move simultaneously
- B. All players know the previous moves ✓
- C. Players have incomplete information
- D. Players use mixed strategies
Why: In a perfect information game, all players know the previous moves made by other players.
Q4. What is a subgame in the context of extensive form games?
- A. A subset of the game tree starting from a node ✓
- B. A player's optimal strategy
- C. A repeated version of the game
- D. A Nash equilibrium
Why: A subgame is a subset of the game tree that starts from a particular node and includes all its descendants.
Q5. What is backward induction used for in extensive form games?
- A. To find mixed strategy equilibria
- B. To solve for Nash equilibria in simultaneous games
- C. To determine optimal strategies by working backwards from the end of the game ✓
- D. To calculate expected payoffs
Why: Backward induction is used to determine optimal strategies by working backwards from the end of the game tree.
Module 7
Module 7: Applications of Game Theory
Applications of Game Theory
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 strategy that guarantees the highest payoff for a player regardless of others\' strategies
- C. A strategy that minimizes the maximum possible loss
- D. A situation where all players cooperate to maximize overall payoff
Why: A Nash equilibrium occurs when no player can benefit by changing their strategy while the other players keep theirs unchanged
Q2. In the prisoner\'s dilemma, what is the outcome if both players play rationally?
- A. Both players cooperate
- B. Both players defect ✓
- C. One cooperates and the other defects
- D. The outcome depends on the game\'s rules
Why: In the prisoner\'s dilemma, if both players act rationally to minimize their own punishment, the outcome is that both players defect
Q3. Which of the following is an example of a zero-sum game?
- A. Chess
- B. Rock-paper-scissors
- C. Both A and B ✓
- D. Neither A nor B
Why: Both chess and rock-paper-scissors are zero-sum games because one player\'s gain is the other\'s loss
Q4. What is the dominant strategy in the prisoner\'s dilemma?
- A. Cooperate
- B. Defect ✓
- C. Randomize between cooperate and defect
- D. Depends on the other player\'s move
Why: In the prisoner\'s dilemma, the dominant strategy for each player is to defect because it leads to a better outcome regardless of the other player\'s choice
Q5. In a game with multiple Nash equilibria, how do players typically choose between them?
- A. Randomly
- B. Based on communication and coordination ✓
- C. By selecting the one with the highest payoff for themselves
- D. By selecting the one with the highest combined payoff
Why: When there are multiple Nash equilibria, players often rely on communication and coordination to choose one that is mutually beneficial