Let's analyze the questions and tables in the images you uploaded.

Question 2

The table provided lists utility values for options across three categories (X, Y, Z). We are told that a person prefers:

• X to Y
• Y to Z
• Hence, X to Z

This means that the utility for X should be higher than the utility for Y, and the utility for Y should be higher than the utility for Z.

Step-by-step analysis of options:

• Option 1: $X = 1$, $Y = 2$, $Z = 3$

  • $Z > Y > X$ (opposite of what we want)

• Option 2: $X = 8$, $Y = 9$, $Z = 10$

  • $Z > Y > X$ (again, opposite of the desired preference)

• Option 3: $X = -10$, $Y = -20$, $Z = -90$

  • $X > Y > Z$ (correct, as it matches the given preference)

• Option 4: $X = -1$, $Y = 0$, $Z = 1$

  • $Z > Y > X$ (again, this doesn't match the desired preference)

Conclusion for Question 2: The correct answer is Option 3.

Question 5

The question asks to classify the type of game described in Question 2. Let's break down the options:

• a. A normal form game: A strategic game represented in a matrix form where players' strategies and payoffs are laid out, which seems to match the format of the table.

• b. An extensive form game: This would be a game represented using a decision tree, which doesn't apply to the format seen here.

• c. A zero-sum game: A game in which one player's gain is another player's loss. However, there is no indication that this is a zero-sum game, as no player-to-player interaction is shown in the matrix.

• d. Both answers a. and c. are correct: Since c. (zero-sum game) doesn't apply, this option is incorrect.

Conclusion for Question 5: The correct answer is a. A normal form game.

Do you need further details on these questions, or would you like clarification? Here are 5 additional related questions for further exploration:

1. How can you identify a zero-sum game in a matrix format?
2. What are the key differences between normal form games and extensive form games?
3. How does utility theory apply to decision-making in economics?
4. How would the solution change if the preferences were reversed (i.e., Z to Y to X)?
5. What strategies can players use in normal form games to maximize their payoffs?

Tip: In game theory, always start by identifying the players, strategies, and payoffs when classifying the type of game you're dealing with!