Sure, the answer is trivial: 100% perfect agent isn't possible. Just have an AI play against itself. Since the game is simultaneous moves, there is no "first move advantage" or anything, so it would play out exactly as a mirror (give or take some random noise in the model). The only thing that would break the symmetry is where food spawns, which also would just be a coin flip which snake it would be close to.
In a 8 player game, it's a little different because there are 'side' and 'corner' positions. Obviously this isn't symmetric anymore, so if you played many games, one position would make itself clearly superior. That likely depends again, on the probability of food appearing in a snakes "zone of control" which you could represent with a voronoi diagram.
My gut instinct is that a 'side' position would eventually be revealed to be stronger because the snake has more options and freedom.
Of course, in a tournament setup, it's fully possible for an AI to have 100% win rate just by random chance, because you are only playing a finite number of games.
More than 2 players adds another level of complexity: alliances. Snake is a bit like Risk in that it's possible to attack a specific player while signalling intent.
We should expect any proper AI to read and understand the others and work out who should be avoided or ganged up on. Rock-Paper-Scissors tournaments have bots that use game moves to recognize eachother and then dump all their points onto a single player -- something similar could happen in Snake as well.
In a 8 player game, it's a little different because there are 'side' and 'corner' positions. Obviously this isn't symmetric anymore, so if you played many games, one position would make itself clearly superior. That likely depends again, on the probability of food appearing in a snakes "zone of control" which you could represent with a voronoi diagram.
My gut instinct is that a 'side' position would eventually be revealed to be stronger because the snake has more options and freedom.
Of course, in a tournament setup, it's fully possible for an AI to have 100% win rate just by random chance, because you are only playing a finite number of games.