A simple answer: iterated elimination of strictly dominated strategies.
The NBA and NHL have an unfortunate scheduling issue: their finals take place at roughly the same time, and having games scheduled at the same time would hurt both of their ratings. But this isn’t a simple coordination game. Everyone wants to avoid playing on Fridays, which is the worst night for ratings. This forces one series to play games on Sundays, Tuesdays, and Thursdays, with the other on Saturdays, Mondays, and Wednesdays. The first series is far more favorable for ratings and advertisements: it avoids the dreaded Friday ans Saturday nights entirely and also hits the coveted Thursday night slot.
So who gets the good slot and why?
Well, the NBA wins because of its popularity. Some sports fans will watch hockey or basketball no matter what, but a sizable share of the population would be willing to watch both. Sadly for the NHL, though, those general sports fans break heavily in favor of the NBA. This allows the NBA to choose its best choice and forces the NHL to be the follower.
A more technical answer relies on iterated elimination of strictly dominated strategies. In my textbook, I have analogous example between a couple of nightclubs, ONE and TWO. Both need to decide whether to schedule a salsa or a disco theme. (This is like deciding whether to schedule games on Saturdays or Sundays.) More patrons prefer salsa to disco. However, ONE has an advantage in that it is closer to town, giving individuals a general preference for it. Thus, TWO really wants to avoid matching its choice with ONE.
We might imagine a payoff matrix like this:
So TWO can still break even if it picks the same choice as ONE but needs to mismatch to make a profit.
How should TWO decide what to do? Well, it should observe that ONE ought to pick salsa regardless of TWO’s choice—no matter what TWO picks, ONE always makes more by choosing salsa in response. Deducing that ONE will pick salsa, TWO can safely fall back on disco.
In the NBA/NHL case, the NHL must recognize that the NBA knows it will draw uncommitted fans regardless of the NHL’s choice. This means that the NBA should pick Sunday regardless of what the NHL selects. In turn, the NHL can safely place hockey on Saturday. It’s not the perfect outcome, but it’s the best the NHL can do given the circumstances.
 Thursdays are the biggest day for ad sales because entertainment companies want to compete for leisure business (movies, theme parks, etc.) over the weekend.
 I used these names in the textbook not only because they represent Player ONE and Player TWO but also because Rochester (where I went to grad school) has a club called ONE. This led to an interesting conversation when the Graduate Student Association scheduled an open bar there. I was relatively new at the time and didn’t know much about the city. After hearing rumors about the vent, I asked a fellow grad student where it would be. “ONE,” she said.
“Yes, I know it’s at 1, but where is it?”
The last two lines repeated more times than I would like to admit.