It is, just not in a head-to-head. Phrase it this way: if you had to read 600 poems and had to pick 200 favorites to award prize money to, was this competition zero sum in the awarding of utility? I thought the answer to this was yes. Perhaps it is no since you aren't reading sets of three and picking one favorite in each set?
We're getting into something else here. Are we seeing how two poets interact, where one of them moves on and the other does not? That's kind of the only way to approach this from a GT perspective, and in fact it will resemble an EGT game, where each of the players is a random poet, interacting with each other at each step in the game. The strategies would have to be "win/lose" for both. The payoff for winning could be 10, the payoff for losing could be -10, and then a tie would result in a 0,0, which would simply send it back into the fray. This would be a zero sum game.
If you're modeling it as one person choosing poems, then you're into decision theory, which is really game theory for single agent games. But that's something else entirely and not really apropos.
But this isn't the same thing as med school admissions.
Say we have 100 seats and 1000 applicants. There is not a fixed number of admission offers that must be made. It is flexible and can change depending on how many excellent applicants the admissions committee sees. That alone eliminates much of the head-to-head-ness of the process, since now if two candidates are down to the last spot, the committee can simply choose to give them both offers of admissions, since it is just as likely that one or both of them will not attend.
We are not whittling down the pool of 1000 applicants to 100, where the other 900 are losers, like with the poems. We are simply making a choice to admit or reject individual students based on A) whether we think they'll actually attend, and B) if they meet our standards (this is simplified, obviously). The applicants are choosing whether to matriculate based on A) if they have any other offers, B) if they would rather go there than not matriculate anywhere, and C) if their other offers are more appealing.
So if you look at it superficially from certain angles, it may seem zero sum. If I don't attend school A and attend school B, I've made a zero sum decision because A loses out on me and B does not. But that's not the game. That's just a consequence of the game. The game is whether or not I (want to) attend and whether or not the school admits me. That is not zero sum, because they don't necessarily lose out if I win. In other words, A_{ij} != -B_{ij} for all i,j.
