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!
I do not think that it is true that it is “very likely” that the solution will be net positive for both players.
In the triangle of possible outcomes, if any of the joint utility points lie in the triangle bounded by x+y>1 (which occupies a quarter of the space of possibilities), then net loss for either player become impossible (and that’s a sufficient, not necessary condition for that).
But if you want, you can restrict to strict Pareto improvements over the default...
True, but points are decreasingly likely to be possible as they become more positive—it’s relatively easy to find trades that are bad ideas, or that have really bad distributions (especially assuming multiple resources, which is presumably why you trade in the first place). They’re also highly correlated: chances are either there are no such points available, or a lot of such points are available.
I’ve looked at it a number of ways, and in each case x+y>1 seems unlikely to exist in a given negotiation unless what is brought to the table is very narrowly defined and the gains from trade are very large relative to quantities traded.
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!
There’s a followup that describes more problems.
In the triangle of possible outcomes, if any of the joint utility points lie in the triangle bounded by x+y>1 (which occupies a quarter of the space of possibilities), then net loss for either player become impossible (and that’s a sufficient, not necessary condition for that).
But if you want, you can restrict to strict Pareto improvements over the default...
True, but points are decreasingly likely to be possible as they become more positive—it’s relatively easy to find trades that are bad ideas, or that have really bad distributions (especially assuming multiple resources, which is presumably why you trade in the first place). They’re also highly correlated: chances are either there are no such points available, or a lot of such points are available.
I’ve looked at it a number of ways, and in each case x+y>1 seems unlikely to exist in a given negotiation unless what is brought to the table is very narrowly defined and the gains from trade are very large relative to quantities traded.