Hi, some game theory homework help please! ### Extensive Form Games of Imperfect InformationConsider the following two extensive form games of imperfect information. For each game:a) Set out the normal form of the game, and find its pure strategy Nash equilibria. b) Find its pure strategy weak sequential equilibria (remember: you have to specify the beliefs of player 2 at his information set).#### Game 1**Description:**This game involves two players. Player 1 makes the first move choosing between L (Left), M (Middle), or R (Right). After M, Player 2 moves with choices ℓ (left) or r (right).**Payoffs:**- If Player 1 chooses L: (2, 4)- If Player 1 chooses R: (3, 1)- If Player 1 chooses M, and Player 2 chooses ℓ: (1, 3)- If Player 1 chooses M, and Player 2 chooses r: (0, 0)**Structure Explanation:**- Player 1's decisions branch at the top.- Player 2's decision branch is under Player 1’s move M, indicated by a dashed line (representing imperfect information).#### Game 2: Selten’s Horse**Description:**This is a three-player game. Player 1 decides first between A (advancing) and D (disengaging). If Player 1 advances, Player 2 decides between L (left) and R (right). If Player 1 disengages, the third player makes a choice.**Payoffs:**- If Player 1 chooses D, and Player 3 chooses L: (0, 0, 0)- If Player 1 chooses D, and Player 3 chooses R: (3, 3, 2)- If Player 1 chooses A, Player 2 at choice 2 chooses L: (4, 4, 0)- If Player 1 chooses A, Player 2 at choice 2 chooses R: (0, 1, 1)- If Player 1 advances directly with action a: (1, 1, 1)**Structure Explanation:**- Player 1's decision initiates the game.- Player 2’s decision, indicated by a dashed line, follows Player 1's advancement.- A branch also allows Player 3 to move if the game proceeds after Player

Given, Two Games: Game1 and Game 2 There is Imperfect information for both the games

Answered: Consider the following two extensive…

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Hi, some game theory homework help please!

### Extensive Form Games of Imperfect Information

Consider the following two extensive form games of imperfect information. For each game:

a) Set out the normal form of the game, and find its pure strategy Nash equilibria.
b) Find its pure strategy weak sequential equilibria (remember: you have to specify the beliefs of player 2 at his information set).

#### Game 1

**Description:**
This game involves two players. Player 1 makes the first move choosing between L (Left), M (Middle), or R (Right). After M, Player 2 moves with choices ℓ (left) or r (right).

**Payoffs:**
- If Player 1 chooses L: (2, 4)
- If Player 1 chooses R: (3, 1)
- If Player 1 chooses M, and Player 2 chooses ℓ: (1, 3)
- If Player 1 chooses M, and Player 2 chooses r: (0, 0)

**Structure Explanation:**
- Player 1's decisions branch at the top.
- Player 2's decision branch is under Player 1’s move M, indicated by a dashed line (representing imperfect information).

#### Game 2: Selten’s Horse

**Description:**
This is a three-player game. Player 1 decides first between A (advancing) and D (disengaging). If Player 1 advances, Player 2 decides between L (left) and R (right). If Player 1 disengages, the third player makes a choice.

**Payoffs:**
- If Player 1 chooses D, and Player 3 chooses L: (0, 0, 0)
- If Player 1 chooses D, and Player 3 chooses R: (3, 3, 2)
- If Player 1 chooses A, Player 2 at choice 2 chooses L: (4, 4, 0)
- If Player 1 chooses A, Player 2 at choice 2 chooses R: (0, 1, 1)
- If Player 1 advances directly with action a: (1, 1, 1)

**Structure Explanation:**
- Player 1's decision initiates the game.
- Player 2’s decision, indicated by a dashed line, follows Player 1's advancement.
- A branch also allows Player 3 to move if the game proceeds after Player

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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