Game Theory Basics Quiz

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Questions and Answers

What is the best strategy for player 1 regardless of player 2's choice?

U (correct)

What will player 2 choose if player 1 selects U?

L (correct)

How are the payoffs represented in two-player strategic form games?

In matrix form (correct)

As a table of values

Through a vector

In a graph

What is player 2's payoff-maximizing strategy dependent on?

Player 1's strategy choice Signup and view all the answers

Which strategy pair is the only sensible outcome of the game described?

(U, L) Signup and view all the answers

What does the term 'dominant strategy' imply in the context of game theory?

A strategy that is beneficial regardless of opponents' strategies Signup and view all the answers

What is the outcome deduced when a game is played by rational players?

The equilibrium outcome based on strategies Signup and view all the answers

What does the notation [$−i$] signify in the context of joint pure strategies?

The strategies of all players except player i Signup and view all the answers

Which concept indicates a more advanced understanding of strategic interaction than merely recognizing payoffs?

Subgame perfection Signup and view all the answers

What characterizes a strategic decision rather than a non-strategic decision?

It requires anticipating the actions of other players. Signup and view all the answers

In a strategic form game, how is the payoff for a player determined?

Through a function of their own strategy and those chosen by other players. Signup and view all the answers

What is an essential feature of a Nash equilibrium?

Each player's strategy is an optimal response to the other players' strategies. Signup and view all the answers

What is the role of unpredictability in strategic decision making?

It arises as players try to maximize their payoffs while considering opponents' strategies. Signup and view all the answers

What distinguishes a Bayesian-Nash equilibrium from a regular Nash equilibrium?

It involves players having beliefs about the types of other players. Signup and view all the answers

Which structure describes the strategic situation involving multiple players and their available strategies?

Strategic form game Signup and view all the answers

In what way is subgame perfection stronger than Nash equilibrium?

It requires rational play in all subgames. Signup and view all the answers

What condition defines a strictly dominant strategy for player i?

It is always better than any other strategy for player i, regardless of opponent's choice. Signup and view all the answers

In the elimination of dominated strategies, what is a characteristic of a strategy that is strictly dominated?

It is never chosen because it yields a lower payoff than another strategy. Signup and view all the answers

If player 1's strategy C is always outperformed by D, what can be inferred about C?

C is a strictly dominated strategy for player 1. Signup and view all the answers

What does the notation $S_i^n$ represent?

The strategies of player i remaining after n rounds of elimination. Signup and view all the answers

Which of the following scenarios illustrates strictly dominated strategies?

Player 2's strategy R always yields a higher payoff than strategy M when Player 1 plays D. Signup and view all the answers

What result can be concluded when both strategies C and M are removed from the strategies set?

Both strategies were strictly dominated by other strategies. Signup and view all the answers

What is the outcome represented by the pair (3, 0) in the context of game strategies?

It indicates the best outcome for player 1 with no payoff for player 2. Signup and view all the answers

Which of the following best describes strategies after the nth round of elimination?

They are the strategies that remain undominated and viable for player i. Signup and view all the answers

What characterizes a strategy that is iteratively strictly undominated?

It belongs to the set of strategies for player i across all iterations. Signup and view all the answers

In game theory, a weakly dominated strategy is defined as one that:

Has at least one comparison where it performs worse than another strategy. Signup and view all the answers

Which strategies are characterized as weakly dominated in the given situation?

D and R are weakly dominated by U and L. Signup and view all the answers

What does the notation $W_i^n$ represent in game theory?

The strategies that survive the nth round of elimination of strictly dominated strategies. Signup and view all the answers

Under what condition does a strategy qualify as iteratively weakly undominated?

It is not weakly dominated in the set of strategies remaining after each elimination round. Signup and view all the answers

What happens to weakly dominated strategies when they are eliminated?

They can make eliminating strictly dominated strategies ineffective. Signup and view all the answers

What is the implication of having no strictly dominated strategies present?

Players have a clearer choice in selecting optimal strategies. Signup and view all the answers

Why is it important to identify both strictly and weakly dominated strategies in a game?

It ensures players can avoid dominated strategies to maximize their payoffs. Signup and view all the answers

What condition must be satisfied for a situation to be considered a Nash equilibrium?

No player can improve their payoff by unilaterally changing their own strategy. Signup and view all the answers

Which statement about pure strategy Nash equilibria is true?

A game may possess more than one pure strategy Nash equilibrium. Signup and view all the answers

How is a mixed strategy defined in the context of Nash equilibrium?

It is a probability distribution over multiple strategies. Signup and view all the answers

In which of the following cases can a Nash equilibrium exist?

When players randomize their choices and have no predictable strategy. Signup and view all the answers

Which of the following describes a scenario where no pure strategy Nash equilibrium exists?

Players have conflicting goals and strategies. Signup and view all the answers

What is the expected utility of both players in the batter-pitcher example when they use mixed strategies?

$0$ Signup and view all the answers

What implication does knowing the opponents' strategy have in playing a Nash equilibrium?

It gives no advantage as changes lead to unpredictability. Signup and view all the answers

Which of the following statements is incorrect regarding the characteristics of Nash equilibria?

All players have complete ignorance of others' strategies. Signup and view all the answers

What does a mixed strategy allow players to do?

Randomize their choices among strategies Signup and view all the answers

In the context of Nash equilibrium, what does the expected utility of player i's strategy represent?

The predicted payoff based on mixed strategies Signup and view all the answers

How is the joint strategy represented in the context of mixed strategies?

As a combination of all players' actions Signup and view all the answers

According to Theorem 7.1, what is one condition for a strategy to be considered a Nash equilibrium?

It must yield at least the same utility as any alternative strategy Signup and view all the answers

What does the term 'incomplete information' refer to in game theory?

Some players are uncertain about others' payoff functions Signup and view all the answers

What is required for a game to be considered under complete information?

Each player's payoff function is known to all players Signup and view all the answers

What does the notation $u_i(m)$ signify in the context of expected utility?

Utility based on mixed strategy outcomes Signup and view all the answers

What fundamentally changes when players use mixed strategies compared to pure strategies?

Strategies can involve randomness Signup and view all the answers

What is a significant outcome of Nash's Existence Theorem?

Every finite strategic form game has at least one Nash equilibrium Signup and view all the answers

Which of the following describes the normal-form representation of a game?

Players' strategies and payoffs are clearly outlined Signup and view all the answers

What is an essential characteristic of a mixed strategy set, $M_i$?

It can represent any pure strategy via probability distribution Signup and view all the answers

Which statement best describes a pure strategy within the context of game theory?

A consistent choice that does not involve randomness Signup and view all the answers

What is the role of each player's utility function in the context of a strategic game?

To determine the payoffs based on chosen strategies Signup and view all the answers

Study Notes

Lecture 1 - Strategic Form Games

Game theory = the systematic study of how rational agents behave in strategic situations.
Each agent must know the others' decisions before determining their own best choice.
Includes concepts like Nash equilibrium, Bayesian-Nash equilibrium, backward induction, and subgame perfection.
Knowing when to apply each concept is important for applied economics.

Lecture 2 - Strategic Form Games under Incomplete Information

Incomplete information = situations where some players are uncertain about other player's payoff functions.
This is different than the standard game's payoff function.
Includes Bayesian games.
Information about others' types.

Lecture 3 - Extensive Form Games

Extensive form = a graphical representation of a game, using a game tree.
The nodes represent decisions and actions.
The lines connecting the nodes represent a logical sequence.
End nodes display payoffs.

Lecture 4 - Extensive Form Games under Incomplete Information

Sequential equilibrium = a solution concept for extensive form games with incomplete information, building on Nash Equilibrium.
It addresses the issue of beliefs in cases where backward induction isn't directly applicable, due to incomplete information.

Lecture 5 - Repeated Games

Deals with games that are played multiple times.
Explores the interactions between players when they know the game will be played many times.

Lecture 6 - Mixed Strategies examples

Mixed strategies = players randomize their choices in a game.
Introduces mixed strategies' Nash Equilibria.

Additional concepts

Iterative elimination of strictly dominated strategies: A method for simplifying games by eliminating dominated strategies, to determine which strategies are rational for players.
Rationality: Players choose strategies that maximize their expected payoffs (given their beliefs)
Common knowledge: A property is common knowledge if everyone knows it, everyone knows that everyone knows it, and so on.
Nash equilibrium: A strategy profile where no player can improve their payoff by unilaterally changing their strategy.
Subgame perfect equilibrium: A Nash equilibrium where every subgame of the game is a Nash Equilibrium
Correlated Equilibrium: A refinement of Nash Equilibrium that allows for correlated strategies, where players' actions may be coordinated.
Bayesian Equilibrium: A refinement of Nash Equilibrium that accounts for beliefs about the other players' types or strategies; used in situations with incomplete information.
Maxmin (and Minmax) strategies: A method for choosing strategies that maximize the minimum possible payoff and minimize the maximum possible loss.

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Description

Test your understanding of key concepts in game theory with this quiz. Explore topics such as dominant strategies, Nash equilibrium, and strategic decision-making. Challenge yourself with questions related to two-player strategic form games and their payoffs.