Optimising table design or optimising the query - mysql

Question

I am trying to decide which one is better: to design a table that wastes a lot of space and has a simple query OR to write a very tight table but then the process of finding what I am looking for would be very processing intense.
The actual problem is this:
Imagine you have a very simple table. 1st column for the ID number the 2nd is a list of names and the 3rd is a list of names too. The 2nd column is a list of people who owe to the people in the 3rd column.
The search should do the following:
I search for a name in the 3rd column and see who owes this person in the 2nd column. A name or multiple names come up, then I want to see who owes them, again a bunch of names come up, and so on to level 5.
Maybe this is a well known scheme for which there is a well known simple answer in table design or MySQL circles. Could anybody suggest a MySQL query or perhaps an appropriate table design where I can use a simple query?
Example
ID owes owned to
1 Peter John
2 John George
3 Abdul George
4 George Anna
So I could design a wasteful table like this
ID 1 2 3 4 5
1 Anna George Abdul
2 Anna George John Peter
3 George Abdul
4 George John Peter
5 John Peter
But this would be very wasteful and bad bad design but it would be very easy to access the data along with the hierarchy and the owing chain.

Answer 1

Something like this seems suitable:
people
+----+--------+
| id | name |
+----+--------+
| 1 | Marty |
| 2 | Steven |
| 3 | John |
+----+--------+
With the table building the relationships between people owed and owing:
loans
+-----------+-------------+
| lender_id | borrower_id |
+-----------+-------------+
| 1 | 2 |
| 1 | 3 |
| 2 | 1 |
+-----------+-------------+
You could get all the people owing a given lender with something as simple as:
SELECT people.id, people.name
FROM loans
INNER JOIN people ON people.id = loans.borrower_id
WHERE loans.lender_id = X
Where X is the id of the lender. Given the lender_id of 1 (Marty) for example would yield:
+----+--------+
| id | name |
+----+--------+
| 2 | Steven |
| 3 | John |
+----+--------+
You can repeat this process for each of the resulting people until there are no results (no one being owed).