Some economics professors may disagree with me on this (no surprise as economists have a habit of disagreeing with each other), but to me it looks as though the NHL falls into the category of both an oligopoly and a bilateral monopoly. Montrealer's point is a good one that could also change the view of this, that there are many other hockey markets outside of North America and the NHL. Going at this on that level, more of a macro one, the analysis of the behavior will be a fair bit different. But probably best just to stick with the NHL as the basis.
The bilateral monopoly idea does hold up. You can lump the NHL and the PA into single entities, a single buyer and a single seller. One obviously wants lower prices, and one higher prices. Their ability to acheive those goals is based on their negotiating power.
But if you narrow the scope a bit and focus on the NHL (and as such the owners), then you have more of an oligopoly. Maybe not one in the truest sense of the definition, but pretty damn close. Fairly low number of businesses, somewhat small percentage of those have a great influence on price, very tough for someone else to enter the market (ie, a new franchise). Non-price competition can also be seen throughout the league.
Another characteristic of an oligopoly that is seen in the NHL has been the topic of many threads and discussions, though not really brought up as such. That would be interdependence. Owners closely watch what decisions the other owners make; in many areas, but it's noticed mostly in the price and benefits of contracts. In this type of market, it is essential that you pay attention to what your competitors do or you will quickly get left behind. In some cases, an owner might choose to not follow his competitors in an effort to try and save what he has (the miser types, you know who those are
). In other cases, some owners simply can't follow the others because they don't have the resources. Either way, you will fall off the pace. There's simply not a way around that in this market (aside from illegal activities). That's why I have never bought into the argument that if most GMs and owners stuck to a budget, then the league wouldn't be in as much trouble as it is now. The way this market acts and reacts, that notion doesn't work in the least little way.
The NHL is a strange animal, to say the least. It's not a conventional market type, tough to separate the parts. I know there are those that would disagree with me, but I believe this to be it's basic set-up. Hope it helps.