The Push and Pull: This is where we encounter the term "mind games" most often. It is everything you do to manipulate your opponent, control space on the stage, creating openings to enable you to land either individual blows or combo starters, how you react and pressure shields, etc.
The Punishment: The end result of all push and pull games. Ranging from individual hits to death combos.
In smash, we still have the same basic fighter concept, and are given an additional component:
The Edge: Encompasses all things related to killing your opponent off the sides and bottom of the stage through guarding the edge. This is where we see gimping most often.
For the Smash series, we have seen the balance shift between the push and pull and the punishment.
In 64, there was a heavy reliance on the combo game, making the push and pull less important than being able to consistently death combo the enemy. The only real importance of the push and pull was to make sure you could land one hit before the enemy. (This is a slightly overstated )
In Melee, there was a balance between the push and pull, and the combo game was significantly more balanced with the addition of DI and the reduction of shield stun. There were so many options regarding movement available that the push and pull became equally important as being able to properly execute the punishment.
In Brawl, we see a huge imbalance in the gameplay. The push and pull game has become far more important than the punishment game, as there is such a weak overall combo system. The problem here is that, while they made the push and pull game so much more important, they slowed down the overall game play and removed many of the movement options, and even inserted an unremoveable random variable (tripping) to further gimp movement. Because of this slower pace, the game becomes boring to watch, as we spend more time in the push and pull, then when we manage to initiate the punishment, there is an epic anti-climactic moment because the opponent can't be punished to an extent that would be fair for their mistake. The game is so oriented towards rewarding camping that, competitively, we will likely see projectile characters stand as far away as possible, then shoot as many things as possible until the opponent approaches, at which point they will exchange very little damage, then resume camping. Close range characters have had their options reduced, as players are punished for approaching by running(your only options from run are to dash attack, grab, or jump. Shielding from run puts you at a disadvantage due to the removal of the first frame running shield and the new lagged shield.), and most characters have a disadvantage by approaching from above. Shield grabbing has been upgraded, given the very small amount of shield hit stun from any move, and at the same time ruined because of the inability to combo out of grab, aside from the few characters that now have nearly skill-less chaingrabs.
I will stop at this point, only because the my purpose here is to explain the imbalance of Brawl and why the mechanisms in this game prevent it from being reasonably viable on a competitive level. Sure, they may continue to play the game in tournament and it may even become big, but it doesn't mean it should be. Brawl has ruined all of the work that we, the melee community, put into getting Smash recognized as a fighting game. Brawl is a platformer party game, not a fighting game.
If anyone disagrees with anything, please feel free to respond with your argument so that I can ruin you. I would further elaborate on what I already have, but I'm starving, and it has probably affected the coherence of some of this post.