Jam Stunna makes a good topic, but I disagree with several of the individual points raised because, if nothing else, they are designed to be specific to fighting games. A theory for competitive value should be all inclusive; you should be able to explain why a game like chess or poker is good for competitive play as easily as you should be able to explain melee or brawl (or refute those games being competitive I suppose).
In order to develop a theory, I'll start by examining some attributes that I believe exist in every competitive games.
1. The primary factor in determining a winner must be decision making. Fighting games usually pass this on the basis that doing the right moves at the right times is a choice, and that's usually what makes the difference at high levels. In chess and the other abstract strategy games, decision making is all that there is really. In the highly random games such as Pokemon or poker, there is still a lot of decision making at every step, and while you have no "guaranteed" winning strategies, better strategies are significantly more likely to win to the point that at high levels the strategies are the most important things in the game.
2. The game in question must be primarily mental. By my definition, physical sports in general fail as competitive games as the primary factor in determining victory in those is the strength of the players (speed, agility, and whatnot are forms of strength don't try to make a stupid objection). In poker, the strategies are what matter, but what if you weren't allowed to look at your cards in the Texas Hold'em variation of poker? That would not be a competitive game; the overwhelmingly most important factor at that point would be randomness. Fighting games could fail here if they became "too technical". That is, if at high levels what REALLY separated players was their ability to make accurate inputs (as opposed to correct inputs), a fighting game would be degenerate and non-competitive. Fortunately, that seems to be rare; I can't find a good example of that.
3. The game must have a sufficiently wide array of plausible decisions such that a "best strategy" is not known even at the highest level. Tic tac toe is the easy example to pick on here; it would be fairly easy to find players who know the perfect strategies so the game cannot be taken seriously as a competitive game. Games of imperfect information or indeterminate outcomes tend to get off easier here, but they can still fail if one factor overwhelms the others. For instance, in Turtles Tournament Fighter (Genesis), every character except Donatello can do an infinite throw loop out of any throw. That game is a degenerate competitive game because all decisions revolve around "land throw loops". Do not that this applies ONLY to real players; a game like checkers may have a perfect strategy known (and before long, chess will be this way too), but since no players are able to remember the entire strategy, it does not necessarily ruin the game at a competitive level.
These are the only three truly universal factors I see in competitive games. They are mental games whose winners are determined by good decisions and in which a perfect strategy is not known by any players. These are indeed the only truly necessary components, but here are some factors that I believe are important for improving an abstract competitive game.
1. All players must have as close to an equal chance of winning as possible. Asymmetric games suffer with this occasionally. In chess, white has a better chance to win or draw than black; chess is still a competitive game, but it would be a better competitive game if the two sides had more similar win/draw/lose rates. 3v1 smash bros is a competitive game in the strictest sense, but it's a really bad competitive game because it's so unfair. Games with a political element such as Risk or Survivor or free for all Smash Bros inherently suffer here; a player can be reduced to a nearly zero chance of winning if the other players simply conspire against him.
2. The entire game should be relevant to the outcome. Monopoly is a good example of a game that fails here; in Monopoly, the game is usually effectively over when less than 25% of the game is complete. One player tends to have the obviously best position, and from that point it is just a matter of process to divine the winner with only fluke luck or various degenerate elements able to take it off track. This is to say that games with "slippery slope" are inherently worse competitive games. Slippery slope will always exist to some extent, but the greater the extent, the more damage it does to the game. Additionally, games with long "pre-game" periods in which the decisions made don't really matter at all would suffer here. Some damage is actually seen commonly in fighting games with overly lengthy combos or super animations; while those combos are being performed or those supers are going off, nothing matters. The game would be better if the damage earned from those were awarded more quickly so "real play" could resume.
3. Cheating must be difficult. Ingame Pokemon is an awful competitive game because of this; it's very easy to cheat by hacking Pokemon and never be caught. Rules such as "no camping" that are really easy to "slightly break" and get away with really hurt a game as the game degenerates into breaking the rules as much as possible without getting punished.
4. The rules must be clearly defined. A dance competition may be competitive in the strictest sense, but dancing is a terrible competitive game since it's very unclear exactly what things constitute winning moves, and in the end the winners will be the ones who match up with the subjective views of the judges just as much as with the objective hard rules of the competition.
5. The game should not reward material advantages. This is inevitable to some extent; fighting games reward finger coordination, and even chess punishes players with severe physical disabilities as they will inevitably require more time to make their moves and thus have less time on their clock. However, the bigger the material advantages, the worse it is. Ingame Pokemon suffers another big blow here as training a team (which is not a part of the actual game since it's an independent activity) grants huge material advantages to the players who do a better job at it (which probably means just investing more time). MMORPGs all suck as competitive games by this criteria as well. Casino style poker (as opposed to tournament poker) even fails here; the richer players have a clear advantage.
6. The game should have standardized rules as much as possible. Monopoly is kinda famous for having various "house rules" that change how the game is played, some of them radically. In fighting games, the usual choice is to choose with an almost religious zeal to use one version of the game with default settings and to viciously reject any alternate versions (it's rude, but it gets the job done). Smash Bros has historically really struggled with this; our community is actually famous for this problem...
7. Avoiding disqualification should be a minimal aspect of the game. Basically, failing to follow the simple rules of the game shouldn't be a big concern. The winner should almost always be the player who played the game the best, not the one who managed to play the game at all. Basketball is a bad game for a lot of reasons, but one of its flaws is that intentionally committing fouls (which are against the rules) is a good strategy as long as you don't do it too much and get disqualified.
This leaves a lot of room up for debate about rules, but it does give us a lot of guidance. By making our two standard versions of play 1v1 and 2v2, we removed all political aspects from Smash Bros which makes the game completely satisfy 2-1. Removing items helped us follow rules 1-1 and 1-2 in the sense that we massively reduced the luck component of the game. Banning a stage like the Temple helps us avoid ruining the game in accordance with 1-3. Using a counterpicking system somewhat helps us on 2-2 (making the character and stage selection portions of the game strategic as well). This could be developed toward the actually controversial issues or toward an analysis of our two competing games, but that would exceed the scope of this topic.
This is only a start; I am not calling this a complete theory and may add more later.
So, I'll probably be posting my essay tomorrow. It's gonna be a DOOZY, too. I apologize in advance to your poor eyes.
