Seeing as javamonk has already linked some good technical articles, I'll try to approach this from more of a theoretical angle.
Arcade game difficulty...
From my own personal experience (not sure there are many or even any articles to back this up but I'll keep looking), arcade games are almost always consistently incremental. Every level the enemies get a set amount stronger, they move a set amount faster, the timer is shortened by a set amount, etc. There are variations to this, like when entirely new enemies or other gameplay elements are introduced at certain points, but in infinite games these will run out eventually.
DDA (Dynamic Difficulty Adjustment) is an interesting difficulty concept that can be found in some arcade games. One good example is Astrosmash. The game gets progressively harder in the form of more and more asteroids, but it can also get a little easier for a short time if the player is struggling.
One example of purely linear difficulty (no DDA) in an arcade game is Robotron: 2084. As the player finishes the levels, enemies progressively become more and more difficult with more and more of them appearing in each level. The game was specifically designed to be extremely difficult and yet people have still managed to "beat" it (after 255 levels the game reverts to the original screen). Not because the developers specifically made it so that it could be beaten, but simply because some people are dedicated enough to do so regardless of the odds (barring the literally impossible).
On that note, if you haven't already, check out The King of Kong. Sort of relevant and offers a bit of an insight into the minds of dedicated arcade gamers who set out to "beat" games (or in this case, high scores).
And now for level design...
This article mostly covers newer games but contains some fascinating insights into level design in general - you might find it helpful and at the very least an interesting read:
This is an article about a technique to manage the difficulty of, well, difficulty. It's scalable to infinite levels and uses DDA concepts:
The information in both of the above articles could be applied to arcade environments - level design tricks to keep people playing, ways to dynamically adjust difficulty so as not to discourage people, etc. You could apply more linear concepts at the same time as well. For example, your game may use DDA in conjunction with a linear difficulty scalar so it consistently increases in difficulty over time while slightly lowering or raising it at certain points based on the player's performance.