The Overseas Housing Allowance (OHA) for military members stationed outside of the United States works a little differently than the stateside housing allowance.
Overseas, military members who live off-base are authorized a maximum amount, based on location and rank. However, the actual amount they receive is based on how much they actually pay for rent and utilities.
For stateside housing allowance, it's possible to rent a cheaper place and pocket the difference; for overseas housing allowance, this is not possible.

