White Box Player Agency

It's All About Style
"The referee is god, at least when it comes to his game..." and it mostly was a "him" back in the day when this phrase was often heard. Obviously there was and maybe still is some truth in that pronouncement. Over the years popular thinking has come to recognize that the game belongs to all the players and not just the referee, however. Empowerment of players can take many forms, some of which I am more comfortable with than others.
One method used to empower players is to make the rules more comprehensive so that the referee is confined to being strictly guided by adherence to predictable, fair rules, thus eliminating as many potentially arbitrary (unfair) rulings as possible. Another approach seen more often in games published independently (indie games) is to make the players equal partners with the referee in everything from world design to developing session storyline at the game table. These are all valid approaches to having fun with the hobby.
White Box has its own brand of player agency, not so much built into the rules as written, but in the flexibility of style of play. I like to be entertained and surprised when I referee and encouraging players to get involved in all aspects of the campaign is one way for me to stay entertained. My "world" or setting is bounded on top and bottom by tall mountain ranges, to left and right by wide seas and what lies beyond is largely undefined. PCs in my world can hail from one of the local, defined cultures or come from outside the known world and therefore their background can be just about anything humans can imagine. Racial choices are set, but cultural choices are limitless. I love asking the question, "What's it like where you come from? Tell me about your home."
White Box being what it is encourages a referee to add to the rules as written, to make stuff up (it's part of the flexibility). I like to try several ways of handling situations at the table and I often ask my players what way they prefer. So the way we handle jumping across a pit in one session may be different than the way we do it in another session based on player input. Consistency within the group and session seems more important to me than across groups, so with one group I may have them roll a simple d6 for success, but with another group at a different table and at a different time may be asked to roll a d20 hoping to roll a number equal to or under their Strength score.
Choosing to roleplay rather than roll dice is another way to empower players to make non-routine choices. Even when dice are involved I like input from my players. After bringing an enemy to zero hit-points with their attack, I frequently ask the player to describe how they defeated their enemy.
We didn't call it a sandbox in the old days, but the concept is as old as the white box itself. I run my game sandbox style in that I present the players with a world and ask them "What do you want to do?" The players decide if they want to explore the dungeon known to be located just outside of town, travel to the sea-port where they hear trouble is brewing, hunt down the local bandits to collect the reward, get involved in the local commerce struggle or what-ever. This style of play requires of the referee both preparation and improvisation, so it may not be the best place to begin. There is always the classic dungeon crawl and with some determination and creativity there's a lot the referee can offer dungeon crawlers.
Whether it's a campaign or a one-off dungeon crawl the white box lends itself to a number of different styles of play, largely dictated by the referee (remember that god thing). The game relies a lot on the referee and a good referee makes all the difference. I think this is true of roleplaying in general, but perhaps more so with the so-called rules lite games. Am I a good referee?  I try to be and that means looking to my players for input, watching for signs that they are having fun and trying to give them the game experience they want.