Thunderdome.
Seriously though, countries set aside neutral battle fields and deploy troops and armor, each with a pt rating based on battlefield effectiveness. Light infantry is less pts then a sniper which is less then a tank etc. These troops will basically have a big ass laser tag fight. Hit enemies by proper weapons will essentially be paralyzed and cannot do anymore in the fight. Last side with people standing, or a particular mutual objective accomplished succeeds (Capture the flag, etc). The outcome determines which side loses the war and must surrender to the winner. This will be a conditional surrender so as a winning side cannot completely strip a country of their wealth and rights or dissolve it completely as some conquerors would do.
as a side note, no soldiers and no weapons is a terrible idea. we shouldn't stop designing technology for warfare. Even if there is world peace, extremeists, psychoes, and would be tyrants can get a surprising amount of support and cause huge problems. There is also the possibility of hostile aliens.
Rather have it and not need it, then need it and not have it.