Cooperative zero-sum two-player game

Question

Is there such a thing as a theory of cooperative zero-sum two-player games (that do not trivially correspond to a non-cooperative one)? The players can never both be benefited by a cooperation, so it seems that rational agents can never have any reason to cooperate on such situation, so the answer seems to be negative.

Answer 1

P.S. not an expert on game theory. If this is incorrect please point that out.

If the game is iterative with high reward for winning and low risk for losing it makes sense to cooperate across iterations.

Also, for the sake of argument, there could be a reason for players to cooperate even in a strictly competitive zero sum game like chess, so long as they share a motivation for doing so. Say you have two impatient chess players who just want to get to the end game, they could just sacrifice pieces in a tit-for-tat strategy until they reach a point where one of them wants to compete