We have always assumed that none of the players are psychic, and that everyone wants everyone to get their fair share

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We have always assumed that none of the players are psychic, and that everyone wants everyone to get their fair share. This project will explore what goes wrong if we break these assumptions: You and your partner treasure hunter have uncovered a box of coins from the ancient civilization of Hyrule. The box contains 2 big coins, 3 silver coins, 4 shiny coins and 5 tiny coins! The two of you decide to split the contents of the box evenly. You and your partner flip a coin and decide that you will have the hard job of being the divider. Then your partner will pick the pile they value more. You took a course in Hylian coins in college, but your partner has never heard of them. You know that each big coin is worth $4, each silver coin is worth $2, each shiny coin is worth $3 and each tiny coin is worth $6

1) According to you, what is the total value of all of the coins? What is your fair share?

2) Divide the coins into two equal piles (pile A and pile B). Your partner will pick one pile and you will get the other pile. In other words, use divide and choose. What coins will you put in each pile? Make sure that you'll be happy with either pile.

3) While you are subdividing the coins, your partner is looking at the coins and informing you of what they think each coin is worth. They think that the big coins are each worth $6, the silver coins are each worth $4, the shiny coins are each worth $5 and the tiny coins are each worth $1 According to your partner, what is the total value of all of the coins? What does your partner think that their fair share is?

4) Look back at the piles that you made in question #2. How does your partner value each pile?

5) You realize that the division you were planning on making is not equal according to your partner. Your partner will be able to get more then what they think their fair share is. Since you know how your partner values things, you can use that knowledge to make a new (unfair) division so that your partner values Pile C more than Pile D, while you secretly think that Pile D is worth more than Pile C. This way, both of you think that you got more than 50% of the total value. What coins will you put in the new piles? (Pile C and Pile D)

6) How do you value the coins that you put in the piles you made in question #5? How does your partner value the piles?