Drupal modules to help with user story
While custom code seems to be good option to achieve the transaction of item ownership, User Points module may help in transaction of items.

In custom way I would have created item as content type with user reference field for item ownership, I would have turned on revision on item content type so to get detailed report of transfer of ownership and on every transaction of item would have updated the ownership field with new owner, maintaining the revisions. User Points module provides handy api's custom integration and it also provides rules integration which looks more robust system to expand user points in future also.