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Chapter 1: Introduction

What is the primary focus of game theory?

Historical events
Mathematical proofs
Philosophical debates
Strategic interactions

Which of the following is NOT a field that game theory has expanded into?

Astronomy
Biology
Computer science
Psychology

In economics, game theory is used to study which of the following?

Plant growth
Weather patterns
Animal behavior
Market competition and pricing strategies

What does the term 'players' refer to in game theory?

The decision-makers involved in the game
The outcomes or utilities that players receive
The situation where no player has an incentive to unilaterally change their strategy
The strategies available to each player

Which of the following is NOT a basic concept in game theory?

Payoffs
Strategies
Players
Gravity

What is a Nash Equilibrium?

A situation where no player has an incentive to unilaterally change their strategy
A strategy that is the best for a player regardless of the strategies chosen by other players
The decision-makers involved in the game
The outcomes or utilities that players receive as a result of their chosen strategies

In a strategic form game, what do the rows and columns of the matrix represent?

Rows represent one player's strategies, columns represent the other player's strategies
Rows represent the decision-makers involved in the game, columns represent the strategies that are the best for a player regardless of the strategies chosen by other players
Rows represent the outcomes or utilities that players receive, columns represent the situation where no player has an incentive to unilaterally change their strategy
Rows represent the payoffs for each player, columns represent the strategies available to each player

What is the Prisoner's Dilemma an example of?

A zero-sum game
A non-zero-sum game
A cooperative game
A stochastic game

Which of the following is NOT a solution concept for TU games?

The core
The Shapley value
The Nash equilibrium
The Bayesian Nash equilibrium

What is the key concept in network games?

The core
The Shapley value
The network structure
The Nash equilibrium

Chapter 2: Basic Concepts of Non-Cooperative Games

What is the primary focus of non-cooperative game theory?

Cooperative interactions where players make decisions together
Games where players are not involved
Strategic interactions where players make decisions independently
Games where players are not aware of their decisions

In a strategic form game, what do the rows and columns of the matrix typically represent?

Rows represent one player's strategies, columns represent the other player's strategies
Rows represent payoffs, columns represent players
Rows represent players, columns represent strategies
Rows represent strategies, columns represent payoffs

What do payoffs quantify in non-cooperative games?

The outcomes or benefits that players receive based on the strategies chosen
The total duration of the game
The complexity of the game
The number of players in the game

In the example game between Alice and Bob, what is the payoff for Alice if she defects and Bob cooperates?

3
5
0
1

What is a Nash equilibrium?

A situation where players do not change their strategy
A situation where no player can benefit by unilaterally changing their strategy
A situation where all players benefit by changing their strategy
A situation where players cooperate

In the example game between Alice and Bob, what is the Nash equilibrium strategy profile?

(D, C)
(C, C)
(D, D)
(C, D)

What does it mean for a strategy profile to be a Nash equilibrium?

Each player's strategy is an optimal response to the strategies of the other players
All players do not change their strategies
Each player's strategy is not an optimal response to the strategies of the other players
All players change their strategies

What is the significance of Nash equilibrium in non-cooperative game theory?

It provides a tool for analyzing cooperative interactions
It provides a tool for analyzing games where players are not involved
It provides a tool for analyzing games where players are not aware of their decisions
It provides a tool for analyzing strategic interactions and predicting the outcomes of non-cooperative games

Chapter 3: Zero-Sum Games

What is the defining characteristic of a zero-sum game?

The total payoff to all players is positive
The total payoff to all players is zero
The total payoff to all players is negative
The total payoff to all players is random

Which of the following is an example of a zero-sum game?

Bridge
Scrabble
Poker
Monopoly

According to the Minimax Theorem, what is the relationship between the maximum expected payoff for the minimizing player and the minimum expected payoff for the maximizing player in a zero-sum game?

The maximum is greater than the minimum
They are equal
They are unrelated
The minimum is greater than the maximum

Which method can be used to solve zero-sum games?

Monte Carlo Simulation
Genetic Algorithms
Neural Networks
Linear Programming

In a zero-sum game, if one player's gain is $5, what is the other player's loss?

$10
It depends on the initial stake
$5
$0

What is the minimax strategy in a zero-sum game?

A strategy where the player always wins
A strategy where the player always loses
A strategy where the player's outcome is random
A pair of strategies where neither player can benefit by changing their strategy unilaterally

Which of the following is NOT a method to solve zero-sum games?

Dynamic Programming
Enumeration
Machine Learning
Linear Programming

In a game of chess, what happens if one player wins?

The game is a draw
The other player also wins
The game continues indefinitely
The other player loses

Chapter 4: Non-Zero-Sum Games

What is the defining characteristic of non-zero-sum games?

Players always lose if the other player wins.
The total payoff for all players is not necessarily zero.
The total payoff for all players is always zero.
Players have identical payoff structures.

Which of the following is an example of a non-zero-sum game?

Zero-Sum Games
Coordination Games
All of the above
Public Goods Games

In the Prisoner's Dilemma, what is the dominant strategy for each suspect?

Defect
Cooperate
Randomly choose
Depend on the other suspect's action

What is the outcome if both suspects cooperate in the Prisoner's Dilemma?

(0, 5)
(3, 3)
(1, 1)
(5, 0)

In coordination games, what happens if players choose different actions?

Neither player benefits.
Both players benefit.
One player benefits while the other loses.
The outcome is unpredictable.

What is the payoff for both drivers if they choose to go straight in the intersection coordination game?

(3, 3)
(1, 1)
(0, 0)
(2, 2)

How many Nash equilibria does the intersection coordination game have?

Two
Four
One
Three

In non-zero-sum games, what does the payoff function determine?

The number of players in the game.
The strategies available to each player.
The outcome for each player based on the strategies chosen.
The total payoff for all players.

Chapter 5: Repeated Games

What is a key feature of finite repeated games?

Players do not interact with each other.
The game has no predetermined number of rounds.
Players can learn from past interactions and adapt their strategies accordingly.
The game ends after a random number of rounds.

Which strategy is used in the Prisoner's Dilemma to encourage cooperation in a repeated game?

Random strategy
Always cooperate
Tit-for-tat
Always defect

What is the Folk Theorem primarily used for in infinite repeated games?

To determine the optimal number of rounds.
To analyze the conditions under which cooperation can be sustained.
To model short-term interactions.
To find the dominant strategy in each round.

What does the Grim Trigger strategy involve?

Always cooperating regardless of the other player's actions.
Always defecting regardless of the other player's actions.
Randomly choosing to cooperate or defect.
Cooperating until the other player defects, then defecting permanently.

In a finite repeated game, what is the dominant strategy in a single-shot Prisoner's Dilemma?

Randomly choose between cooperate and defect
Defect
Use tit-for-tat
Cooperate

What is the main challenge in infinite repeated games?

Finding strategies that are sustainable over an infinite number of periods.
Analyzing the conditions under which cooperation can be sustained.
Determining the optimal number of rounds.
Modeling short-term interactions.

Which of the following is NOT a key aspect of repeated games?

Players do not interact with each other.
Decisions are made sequentially.
Players can learn from past interactions.
Players can condition their actions on the history of play.

What is the purpose of trigger strategies in repeated games?

To find the dominant strategy in each round.
To commit to a particular course of action unless a deviation occurs.
To model short-term interactions.
To determine the optimal number of rounds.

Which theorem provides a tool for analyzing infinite repeated games?

Zero-Sum Game Theorem
Folk Theorem
Minimax Theorem
Nash Equilibrium

In the context of repeated games, what does 'subgame-perfect equilibrium' refer to?

A strategy where players always cooperate.
A strategy where players always defect.
An equilibrium strategy profile where all strategies are optimal given the history of play.
A strategy where players randomly choose between cooperate and defect.

Chapter 6: Stochastic Games

What is the key feature of stochastic games?

The game always has a unique Nash equilibrium.
The game's state evolves deterministically.
Players always have complete information about each other's actions.
Players do not have perfect information about the game's state or the actions of their opponents.

Which of the following is an example of a stochastic game?

Monopoly
Poker
Chess
Tic-Tac-Toe

What is the concept of Markov perfect equilibrium (MPE) in stochastic games?

A strategy profile where each player's strategy is optimal given the strategies of the other players and the game's stochastic dynamics.
A strategy profile where each player's strategy is optimal given the strategies of the other players and the game's deterministic dynamics.
A strategy profile where each player's strategy is optimal given the strategies of the other players and the game's complete information.
A strategy profile where each player's strategy is optimal given the strategies of the other players and the game's static dynamics.

In what method is an MPE typically found in stochastic games?

Forward induction
Induction by elimination
Simultaneous induction
Backward induction

What is a signaling game in the context of stochastic games?

A game where all players have complete information about each other's actions.
A game where players do not have any private information.
A game where one player has private information that they can send to another player in the form of a signal.
A game where the state of the game evolves deterministically.

In which field are stochastic games commonly used to model the behavior of firms?

Chemistry
Biology
Economics
Physics

What is a Bayesian game in the context of stochastic games?

A game where players do not have any beliefs about the type of the other players.
A game where all players have the same beliefs about the type of the other players.
A game where players have different beliefs about the type of the other players, and these beliefs are updated as the game progresses.
A game where players have complete information about each other's actions.

What is the primary purpose of introducing randomness into the game's dynamics in stochastic games?

To ensure that the game always has a unique Nash equilibrium.
To eliminate uncertainty from the game.
To capture the complex interactions between players in a more realistic way than traditional games of complete information.
To make the game easier to solve.

Chapter 7: Evolutionary Game Theory

What is the key concept in Evolutionary Game Theory that describes how the frequency of different strategies changes over time?

Zero-Sum Game
Replicator Dynamics
Nash Equilibrium
Mixed Strategies

Which of the following is the correct replicator dynamics equation?

ẋ_i(t) = π(x(t)) - π_i(x(t))
ẋ_i(t) = π_i(x(t)) - π(x(t))
ẋ_i(t) = x_i(t) [π_i(x(t)) - π(x(t))]
ẋ_i(t) = x_i(t) * π_i(x(t))

What does the term 'Evolutionarily Stable Strategy' (ESS) refer to?

A strategy that is randomly chosen by the population
A strategy that, if adopted by a population, cannot be invaded by any alternative strategy
A strategy that always leads to the highest payoff
A strategy that is always dominated by another strategy

Which of the following is a correct condition for a strategy s* to be an Evolutionarily Stable Strategy?

π(s*, s*) = π(s, s*) and π(s, s) = π(s*, s)
π(s*, s*) < π(s, s*) and π(s, s) > π(s*, s)
π(s*, s*) > π(s, s*) and π(s, s) > π(s*, s)
π(s*, s*) > π(s, s*) or [π(s*, s*) = π(s, s*) and π(s, s) < π(s*, s)]

In which area is Evolutionary Game Theory most commonly applied to study the dynamics of strategic interactions?

Chemistry
Linguistics
Economics
Physics

Which of the following is an example of an application of Evolutionary Game Theory in economics?

Studying the evolution of human language
Exploring the behavior of subatomic particles
Analyzing the structure of the DNA molecule
Studying the evolution of pricing strategies in oligopolistic markets

What is the primary focus of Evolutionary Game Theory?

Finding the optimal strategy for a single player
Analyzing the stability of a system of strategies
Predicting the outcome of a one-shot game
How strategies evolve over time as players adapt to the strategies of others

Chapter 8: Mechanism Design

What is the primary goal of mechanism design?

To maximize the utility of individual agents.
To minimize the complexity of interactions.
To predict the behavior of self-interested agents.
To design rules of interaction to achieve desired outcomes.

Which of the following is a key concept in mechanism design?

Incentive compatibility
Mechanism implementation
Game theory equilibrium
Utility maximization

What does the revelation principle state?

Incentive compatibility is not necessary for mechanism design.
For any mechanism, there exists an equivalent direct mechanism that achieves the same outcome and is also incentive compatible.
Mechanisms must always be indirect to be effective.
The revelation principle is only applicable to voting systems.

Which auction format involves bidders successively bidding higher prices?

Sealed-bid Auction
English Auction
Dutch Auction
Vickrey Auction

In a Vickrey Auction, the winner pays:

The second-highest bid
The average of all bids
A fixed price determined by the auctioneer
The highest bid

Which voting system requires voters to approve of a subset of candidates?

Approval Voting
Ranked-Choice Voting
Majority Judgment
Plurality Voting

What is the primary criterion for individual rationality in mechanism design?

Each agent prefers participating in the mechanism to not participating.
The mechanism must maximize social welfare.
Each agent must reveal their true type.
The mechanism must be strategy-proof.

Which of the following is NOT a common auction format?

Dutch Auction
First-price sealed-bid auction
English Auction
Vickrey Auction

In mechanism design, what does 'direct mechanism' mean?

A mechanism where agents report their types truthfully.
A mechanism where agents are not self-interested.
A mechanism where the designer controls all outcomes.
A mechanism where agents do not report their types.

Which of the following is a fundamental result in mechanism design?

The Nash equilibrium
The Pareto efficiency
The revelation principle
The zero-sum game

Chapter 10: Advanced Topics in Non-Cooperative Game Theory

In Bayesian games, what represents a player's private information?

Type
Utility
Strategy
Payoff

What is the solution concept for Bayesian games?

Nash equilibrium
Dominant strategy
Pareto efficiency
Bayesian Nash equilibrium

In signaling games, who has private information that they can reveal to another player?

Neither signaler nor receiver
Receiver
Both signaler and receiver
Signaler

What is the key aspect of signaling games?

Type
Network structure
Payoff
Cost of signaling

In network games, what determines the players' interactions and influences their strategic choices?

Type
Cost of signaling
Payoff
Network structure

What is the solution concept for network games?

Network Nash equilibrium
Bayesian Nash equilibrium
Nash equilibrium
Pareto efficiency

Which of the following is a subclass of Bayesian games?

Cooperative games
Signaling games
Zero-sum games
Non-zero-sum games

In network games, what do players' strategies and payoffs depend on?

The cost of signaling
The network structure
Actions of their neighbors in the network
Their own type

What is the goal of the signaler in signaling games?

To minimize the cost of signaling
To ensure the receiver's best decision
To maximize their own payoff
To influence the receiver's decisions based on the private information

Which of the following is NOT an application of signaling games?

Biological networks
Advertising and marketing strategies
Economics
Modeling the spread of information in social networks

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Game Theory: Non-Cooperative Game Theory

Chapter 1: Introduction

Chapter 2: Basic Concepts of Non-Cooperative Games

Chapter 3: Zero-Sum Games

Chapter 4: Non-Zero-Sum Games

Chapter 5: Repeated Games

Chapter 6: Stochastic Games

Chapter 7: Evolutionary Game Theory

Chapter 8: Mechanism Design

Chapter 10: Advanced Topics in Non-Cooperative Game Theory

Readings

Gallery

Econometric Society

Game Theory Society

Harvard University

Institute for Advanced Study

John Harsanyi

John Nash

John von Neumann

Lloyd Shapley

National Bureau of Economic Research

Oskar Morgenstern

Princeton University

RAND Corporation

Reinhard Selten

Robert Aumann

Roger Myerson

Stanford University

Thomas Schelling