The problem involves four players (Abe, Betty, Cory, and Dana) who are dividing assets into four shares ($s_1$, $s_2$, $s_3$, and $s_4$). The table provided shows the percentage of total asset value for each share that is assigned to each player.

The table is as follows:

We need to use this information to answer a set of questions, starting with:

(a) Which of the shares are fair shares for Abe?

Explanation of "Fair Shares":

A "fair share" for a player is when the total value assigned to that player (across all shares) adds up to at least 25%. Since there are four players, each player should expect a fair division to be at least $\frac{1}{4} = 25\%$ of the total asset value.

Now let's analyze Abe's situation:

• $s_1 = 22\%$
• $s_2 = 28\%$
• $s_3 = 24\%$
• $s_4 = 26\%$

Since a fair share means receiving at least 25%, the shares that Abe considers "fair" would be $s_2$ (28%) and $s_4$ (26%), as these shares give him at least 25% of the total value.

Conclusion for part (a):

The fair shares for Abe are $s_2$ and $s_4$.

Would you like to proceed with other parts of the question, or go into more detail on this?

Here are some related questions:

1. What are the fair shares for Betty?
2. What are the fair shares for Cory?
3. What are the fair shares for Dana?
4. How would you calculate the fair share for each player mathematically?
5. If the total percentage for a player is less than 25%, how would you recommend dividing assets to adjust fairness?

Tip: In fair division problems, if a player's total is less than 25%, negotiations or adjustments are necessary to redistribute shares equitably.