**Game Description:**Players 1 and 2 are tasked with deciding whether or not to carry an umbrella when leaving home. Here's how the game is structured:- There is a 50-50 chance of rain.- Each player has different payoffs based on the weather and their decision: - $-5$ if a player does not carry an umbrella and it rains. - $-2$ if a player carries an umbrella and it rains. - $-1$ if a player carries an umbrella and it is sunny. - $1$ if a player doesn’t carry an umbrella and it is sunny.**Information Asymmetry:**- Player 1 knows the weather condition before leaving home.- Player 2 does not know the weather, but can observe Player 1's decision (whether they carry an umbrella or not).**Objective:**- Give the extensive and strategic forms of the game.- Find the Nash equilibria.- Determine if the game is dominance solvable.**Game Analysis:**To solve this game, consider these steps:1. **Extensive Form:** - Construct a decision tree illustrating the sequential nature of decisions, starting with the weather, followed by Player 1's decision, and lastly Player 2's decision.2. **Strategic Form:** - Create a payoff matrix detailing the strategies and corresponding payoffs for both players.3. **Nash Equilibria:** - Identify strategy combinations where neither player benefits by unilaterally changing their strategy, given the strategy of the other player.4. **Dominance Solvability:** - Analyze if the game can be simplified by iteratively removing dominated strategies, leading to a single strategy for each player.

Game theory is the study of how interdependent decisions made by economic agents result in outcomes…

aving ne. I and z must decide whether or not to carry an how that there is a 50-50 chance of rain. Each player's payoff is -5 if he does not carry an umbrella d it rains, −2 if he carries an umbrella and it rains, -1 if he carries an umbrella and it is sunny d 1 if he doesn't carry an umbrella and it is sunny. Player 1 learns the weather before leaving me; player 2 does not, but he can observe player 1's action before choosing his own. Give the tensive and strategic forms of the game and find its Nash equilibria. Is it dominance solvable?

aving ne. I and z must decide whether or not to carry an how that there is a 50-50 chance of rain. Each player's payoff is -5 if he does not carry an umbrella d it rains, −2 if he carries an umbrella and it rains, -1 if he carries an umbrella and it is sunny d 1 if he doesn't carry an umbrella and it is sunny. Player 1 learns the weather before leaving me; player 2 does not, but he can observe player 1's action before choosing his own. Give the tensive and strategic forms of the game and find its Nash equilibria. Is it dominance solvable?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Game Description:**

Players 1 and 2 are tasked with deciding whether or not to carry an umbrella when leaving home. Here's how the game is structured:

- There is a 50-50 chance of rain.
- Each player has different payoffs based on the weather and their decision:
- $-5$ if a player does not carry an umbrella and it rains.
- $-2$ if a player carries an umbrella and it rains.
- $-1$ if a player carries an umbrella and it is sunny.
- $1$ if a player doesn’t carry an umbrella and it is sunny.

**Information Asymmetry:**

- Player 1 knows the weather condition before leaving home.
- Player 2 does not know the weather, but can observe Player 1's decision (whether they carry an umbrella or not).

**Objective:**

- Give the extensive and strategic forms of the game.
- Find the Nash equilibria.
- Determine if the game is dominance solvable.

**Game Analysis:**

To solve this game, consider these steps:

1. **Extensive Form:**
- Construct a decision tree illustrating the sequential nature of decisions, starting with the weather, followed by Player 1's decision, and lastly Player 2's decision.

2. **Strategic Form:**
- Create a payoff matrix detailing the strategies and corresponding payoffs for both players.

3. **Nash Equilibria:**
- Identify strategy combinations where neither player benefits by unilaterally changing their strategy, given the strategy of the other player.

4. **Dominance Solvability:**
- Analyze if the game can be simplified by iteratively removing dominated strategies, leading to a single strategy for each player.

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