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.
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.