I do not think that it is true that it is "very likely" that the solution will be net positive for both players. If players have a variety of marginal utilities from resources, it seems reasonable to expect that this will cause most 'negotiations' to result in pure redistribution, and there are many cases (such as Wei_Dai's second example) where one can simply lose all their resources.

It also seems like a very bad assumption for agents to assume that they'll be exposed to these situations symmetrically; most agents should be able to have a rough idea where they lie on the spectrum compared to their likely trading partners.

More than that, in a world where this was an enforced negotiating style, it seems that you have a dystopia where the best way to gain utility is do a combination of modifying your utility function such that you gain transfers of resources, and/or seeking out trading partners who will be forced to give you resources, and that such efforts will rapidly consume a growing share of the resources. That is certainly what happens when I game out a real world test, with Omega enforcing the rules!