In many historical movies the kings often meet up before fighting each other in a battle. Most of the time they're just calling each other names before returning to their armies. Maybe this is mostly the case in fiction movies - but if it really happened what kept them from assassinating each other during these encounters?
I'm not sure - but if I remember correctly from the time of studying history kings would often meet up as the armies marched towards each other.
Quite often it would result in negotiations of surrender if the other king was hopelessly outnumbered and/or his army was highly demotivated. However often it wasn't actual arranged battles, the code of honor was not as in the movies and surprise attacks were more efficient tools of war.
Killing your opponents king would go against your own interests, because you'd end up killing what the people were there to fight for, and the whole reason for having a parlor was to prevent more losses than necessary. The king didn't lead the battle as you often see, it would divided into many divisions each led by someone respected. 'Chiefs', 'Noblemen' etc. and by killing a king you'd only end up pissing the masses off and securing there would be a battle.