Game Theory Problem dealing with personal choices

Problem 1 1. Suppose you and one of your two roommates have just finished cleaning your dorm suite and found 13 quarters which you put on a table in the middle of the room. The third roommate who did none of the cleaning comes in from an afternoon of fun and relaxation and proposes that you divide the coins up the following way: The two who cleaned and collected the quarters will take turns after flipping a coin to see who goes first. At each turn the player has a choice to take 1 or 2 quarters. If the player takes 1 coin, then the next player gets a turn. If the player takes 2 coins, then the game ends and the third roommate gets the rest of the money on the table. a. Th... click for more

Cutting a Cake-Game Theory Problem dealing with personal choices

Problem dealing with cutting a cake and personal choices Problem 2 There is a cake that is half lemon and half coffee. Steve values a whole lemon cake at $6, and a whole coffee cake at $10. Kevin values a whole lemon cake at $6 and a whole coffee cake at $4. Professor Raiffa suggests that they should divide the cake by selecting one person to cut the cake any way they like and the other person to choose whatever piece he prefers. a. If Steve is selected to cut the cake, and he does not know Kevin’s preferences, how should he cut the cake (assuming he is rationally trying to maximize his expected value)? What will the outcome be for both players? Suggestion: draw the cake and ... click for more

Allocation between two persons of a list of items and their preference

This is an allocation of ten estates between two individuals

Statistics: Percentages from Groups and Venn Diagrams

When the members of the Eye and I Photo Club discussed what type of film they had used during the past month, the following information was obtained; 77 used black and white film, 24 used only black and white, 65 used color, 18 used only color, 101 used black and white or color, 27 used infrared, 9 used all three types, and 8 didn't use any film during the past month. a) What percent of the members used only infrared film? and b) What percent of the members used at least two of the types of film?

Modern/Abstract Algebra Problem (Group Theory)

Show that the group generated by two elements where all the elements have order 3 is finite.