Game Theory: Ruling Out Dominated Strategies

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Questions and Answers

What is a key element of a game in the context of strategic interactions?

Strategy sets (correct)

Player emotions

Historical decisions

Randomness in outcomes

In which form is a game typically displayed as a matrix?

Simulated form

Strategic form (correct)

Extensive form

Comprehensive form

What does the term 'strictly dominate' refer to in strategic situations?

One strategy being inferior to another

One strategy resulting in better payoffs regardless of opponents' actions (correct)

A strategy that always results in a lower payoff

A strategy that is never played

Why might randomizing between two strategies be advantageous?

It can strictly dominate a third strategy Signup and view all the answers

What distinguishes a game presented in extensive form from one in strategic form?

It shows the sequence of events Signup and view all the answers

What does it mean for a strategy to strictly dominate another strategy for Player 1?

It yields higher payoffs against every possible strategy of Player 2. Signup and view all the answers

In the example provided, what is the outcome for Player 1 if Player 2 chooses Stay2 while Player 1 chooses Stay1?

Player 1 receives a payoff of 4. Signup and view all the answers

Under what condition does ruling out strictly dominated strategies suffice for making predictions in a game?

In some games, it is enough for making sharp predictions of the outcome. Signup and view all the answers

Which of the following statements is true regarding a dominant strategy?

It is always the best choice regardless of the opponent's strategy. Signup and view all the answers

What is the payoff for Player 2 if Player 1 chooses Go1 and Player 2 chooses Go2?

<ol start="0"> <li></li> </ol> Signup and view all the answers

If Player 1 plays Stay1, what are Player 2's payoffs if they play Stay2?

4, 0. Signup and view all the answers

What will be the outcome if Player 1 chooses Stay1 and Player 2 chooses Go2?

Player 1 receives 4 and Player 2 gets 0. Signup and view all the answers

Which strategy for Player 2 strictly dominates Go2?

Stay2. Signup and view all the answers

What does it mean for a strategy to be strictly dominated?

It results in a lower payoff compared to another strategy, regardless of opponents' actions. Signup and view all the answers

Why do we rule out strictly dominated strategies when predicting game outcomes?

Rational players will not choose them since better options exist. Signup and view all the answers

Which assumption is always made about players in a strategic game?

Players will always act in a way that maximizes their own payoff. Signup and view all the answers

What is implied by stronger assumptions about players' beliefs?

Players have accurate beliefs about how others will act. Signup and view all the answers

What is typically represented in a player's information set during a game?

The beliefs players hold about each other's rationality. Signup and view all the answers

What best describes the term 'strictly dominated strategies'?

Strategies consistently outperformed by other strategies. Signup and view all the answers

What must players believe about their opponents for predictions to be valid?

Opponents are rational as well. Signup and view all the answers

In the context of game theory, what does making predictions based on stronger assumptions imply?

Predictions become clearer and more reliable. Signup and view all the answers

What is meant by strictly dominated strategies in game theory?

Strategies that yield lower payoffs than another strategy, regardless of the opponent's choice. Signup and view all the answers

In the Real Estate Bubble Game examples provided, which strategy for Investor 1 yields a higher payoff at Time 2?

Time 1. Signup and view all the answers

Which of the following describes weak dominance?

When a strategy never performs worse and sometimes performs better than another strategy. Signup and view all the answers

What assumption is emphasized regarding player behavior in the context of strict dominance?

Players act rationally and do not use strictly dominated strategies. Signup and view all the answers

In the provided examples, what is the outcome for Investor 2 when Investor 1 selects Time 3 and Investor 2 selects Time 3?

-3, -3. Signup and view all the answers

What does the inverse demand curve represent in the Cola Wars example?

The quantity of a product demanded at different price levels. Signup and view all the answers

What strategy should Coke use according to the algebraic demonstration of strict dominance?

Any quantity less than 30. Signup and view all the answers

Why is it useful to recognize strictly dominated strategies in a game?

It narrows down the strategy selection for players. Signup and view all the answers

Study Notes

Making Predictions by Ruling Out Dominated Strategies

Key elements of a game: Players, strategy sets, and payoff functions are foundational components known to players.
Two ways to represent a game: Strategic form (matrix for two players and few strategies) and game tree (extensive form for sequential events).
Concept of players’ information sets highlights how players’ decisions depend on the knowledge of each other’s strategies.

Definition of "Strictly Dominate"

A strategy is strictly dominated for a player if it yields a lower payoff than another strategy in every possible scenario.
Example: In a game, if Player 1’s “Stay1” yields better outcomes compared to “Go1” when evaluated against Player 2’s strategies (Stay2 and Go2).

Ruling Out Dominated Strategies

Ruling out strictly dominated strategies can sharpen predictions for outcomes in games.
A player has a dominant strategy if it is strictly better than any other strategy, regardless of what opponents choose.
In some scenarios, merely excluding strictly dominated strategies does not guarantee clear predictions and may require additional assumptions.

Implications for Rationality

All players are assumed to be rational, influencing their beliefs about opponents’ rationality.
Strengthening assumptions about players’ beliefs can lead to clearer expectations of strategies.

Weak Dominance

Weak dominance occurs when a strategy is at least as good as another in some scenarios and better in others, but not across all situations.
Randomizing between two strategies can strictly dominate a third strategy, showing the complexity of strategic choices.

Practical Applications: The Real Estate Bubble Game

The game includes a payoff matrix reflecting investors’ possible strategies over several time periods.
Recognizing strictly dominated strategies helps narrow down viable options before making predictions about outcomes.

Cola Wars Example

In the context of Coca-Cola and Pepsi, altering quantity strategies can yield dominant strategies based on algebraic calculations of payoffs.
Understanding payoff functions graphically and algebraically aids in identifying dominant strategies in competitive scenarios.

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Description

Explore the fundamentals of game theory, focusing on predicting outcomes by ruling out dominated strategies. Understand the key elements of games, including player strategies and payoff functions, and learn the importance of strictly dominated strategies in making strategic decisions.