The Assignment Problem
The assignment problem is a one-sided version of the matching
market. For example: The objective is to match individuals to positions.
It can be set up as an lp in the same way as the matching market.
There are two versions:
- Position constraints. The “profits” to positions are what
the individuals pay for the position, the “wage” is remaining
surplus, that they keep.
- No constraints. Model this as more positions of each type
than there are agents in the economy. Then the position price
will be 0 and individuals keep all the surplus. Here the focus
is on self-selection and the match. An example of this is the
Roy (1951) model.