Sports
What you describe is a sports tournament.
People meet, compete, somebody wins. And then everybody hug and go home.
People do this today in fencing, kendo and other martial arts.
As @Baldrikk wrote in a comment, in medieval times, they had tournaments which would look very much like a battle. Though in those days people dying in a tournament was not uncommon so this may a bit fierce for your purpose.
In between the tournaments, people train with others on their own team. This training can get pretty fierce too.
The prize can be those rare resources suggested by others.
There will be rules, the most important will be "No Killing or Maiming!" The penalty should at least be that the guilty part can no longer take part in these tournaments.
People on both sides have heard that once long ago people were actually fighting seriously over these resources. Both sides agree that the sports tournament is a better idea.