You always hear about wars or political backstabbing, but when they aren't off playing soldier out hunting with their buddies, what do the heads of state in the middle ages actually do? Is there an expectation that they have day-to-day responsibilities to the state? Are they more pre-occupied with their own personal economic gain? I assume they have some source of wealth otherwise they wouldn't have been powerful enough to become kings in the first place. I've read that feudalism is overstated, but to what extent are kings (and queens!) actually engaged in domestic policy?
You assume that 'playing soldier' and 'hunting with their buddies' is not work?
Leading armies was a major responsibility of a king, as it wasn't like modern armies where people sign up for a term of enlistment. It was a lot closer to a major election campaign, where the king had to convince, threaten, beg, etc his allies and vassals to contribute soldiers and treasure for the campaign. Leading the army in the battle and giving a fancy speech was just a minor part of it.
Going hunting with your buddies isn't just a waste of time. This is politics. The king's buddies are often very powerful and influential ministers and lords in their own right. Going hunting was about showing off your wealth and influence (it can be very expensive!) and making deals and building relationships between important people. You have to remember that it was the dynasty or family that was important, and treaties were made between individuals, not between nation-states as we might think today. You'd have a personal alliance with the Duke of Anjou, and if he fell off his horse and died you would have to renegotiate a relationship with whoever succeeded him.
In the early medieval period especially most kings did not just sit on their throne - their entire court was traveling around the realm as a way to 'show the flag' and to express his power and visit various nobles to 'rule'. The king's court was often too expensive for any one castle to maintain so they would travel frequently and be hosted by various other important personages for a time, where the king would make deals.
Really every kingdom and king is different, and the idea of a codified idea of a hierarchical structure isn't really true. Some kings wielded more absolute power while others were often overshadowed by people who were supposed to be their underlings. The primary job of a king was keeping his throne and passing it to his heir - a difficult task in the best of times!
/u/sunagainstgold has previously answered In medieval times what were the daily activities of royalty? with additional input from /u/idjet.
Note that this answer was originally published several years ago. More answers for the OP would be wonderful.
The subreddit FAQ has a section about the nature of feudalism