Thanks for your explanation. This is my explanation.
The "island" would be Earth and all it's political systems because your analogy is describing world trade.
The people of the world live in their respective political systems, and they have to have things to live. Some systems provide more abundance to answer the needs than others.
The political systems reflect the people who live in them because those same people either create the system by commission, or allow the system to form by omission. Their aggregate mass is always greater than that of their leaders. If that aggregate mass can't cooperate enough to build a mutually enriching place to live, that's their problem, not any others who may be doing better.
We have brutal (hard and soft) regimes, which the people have allowed to rule them, taking much and returning little. A democratic republic, if it is to stay a free and sovereign system, cannot compete economically with a brutal regime.
If trade is globally designed, democratic republics, our (American) way of life incidentally, must turn into brutal regimes to provide for basic needs of their peoples.
Trade is naturally internal to a political system for the security and benefit the people of that system. It's proven so because internal trade is archetypical of all trade. If it is distorted to a global level where its basic maxims don't apply, there must be a global government to enforce any inequity.
If you were to provide each of your desert islanders with a commodity generator powered by how creatively their owners pounded sand, your analogy would have the proper form for analysis.