I have participated in a few AI programming competitions (where the AI control simple programs, robots, ants, etc) and they generally turn into a few weeks of wonderful ideas followed by discovery of a degenerate case in the rules set.
(For example, in a beautiful simulation where a single program had to control a colony of ants who did not have any room for state other than a current instruction pointer and the input of their senses, someone successfully identified an algorithm to have each ant figure out which ant they were, and then execute a pre-planned sequence of moves to wall in the entire enemy base, faster than any non-degenerate program could possibly counteract it. It was beauty to behold but it also crushed the life out of the community -- the best ant has been crowned, everyone else gets to play for second best.
This is, of course, a universal problem in game design. The answer is to iterate on the rules. I don't play WoW, for much the same reason that I've never tried heroin, but I have heard the term to nerf; it was obviously invented by people whose killer strategies were neutralized by a new iteration of the rules.
With luck you eventually discover chess or Go: a game with no obvious degenerate case in the rules. But that takes lots of design work.
My suspicion is that writing AIs is so much work, and the player base is so rarefied, that there's not quite enough energy to support a game that evolves quickly enough to be constantly escaping from the degenerate case of the week, wandering through game-design space in search of the next chess. But I suppose that could change. There didn't used to be a core audience for a card game whose rules and cards changed constantly, but now there apparently is.
I am fairly sure that for any non-trivial game that would boil down to a solution to the halting problem, though I lack time to prove it.
(Or possibly what I think of as the "finite halting problem" somewhat colloquially; a system that isn't actually Turing Complete because it's finite and bounded, but shares "enough" aspects of Turing Completeness that it still means that it's completely computationally infeasible to "prove" the property in question in the real world. Technically the halting problem on real computers falls into this class, a program running without IO is technically on a finite state machine but you're still not going to solve even that halting problem in a world where the bidding opens at 4GB of RAM.)
This is going to be like the second half of a joke about a mathematician and an engineer walking into a bar....
... but, to objectively evaluate whether a game has a degenerate winning condition, make it good enough that twelve-year-olds want to play it, then wait a month or two. ;)
Corewar might be worth looking into. I don't think it has hit a degenerative case yet, or if it has, it has lasted pretty long.
The hill (when Corewar is played king of the hill style on the internet) could be considered the environment. Of course different kinds of hills could be envisioned, for example arranging warriors on a grid.
What also tends to happen is that you stumble upon a project after it has existed for a while and there are already AI's with PhD-grade algorithms around, that are impossible to beat without investing a huge amount of time. That tends to demotivate people. It would be nice if you could develop a contest where such a thing is impossible and even an unsophisticated AI wins some of the time, for instance because the context is manipulated such that being sophosticated is far from optimal strategy.
One possibility that would solve both of those problems is periodically changing the rules. Minor adjustments as needed to make sure nobody finds a way to totally exploit the system, and maybe a major monthly rule-change.
Perhaps if one of the games was a simple 'capture the flag' which could reset, it would avoid this problem? You wouldn't be competing against those awesome players all the time. A round would start, 10 players would be selected for each team (randomly or based on pre-organized teams). The actions could be as simple as, Look, Move, Shoot, Take Flag.
(For example, in a beautiful simulation where a single program had to control a colony of ants who did not have any room for state other than a current instruction pointer and the input of their senses, someone successfully identified an algorithm to have each ant figure out which ant they were, and then execute a pre-planned sequence of moves to wall in the entire enemy base, faster than any non-degenerate program could possibly counteract it. It was beauty to behold but it also crushed the life out of the community -- the best ant has been crowned, everyone else gets to play for second best.