I don't see how markets are supposed to solve that when we allow countries with slaves to participate on the markets. Or landlords to exercise economic rent over the land that other people maintain and live on. I guess my point here is I'm not sure markets as we have them today solve that problem very well anyway.
> Equal number of people doesn't not solve the principle agent problem.
But it does. If your claim is that every person is an economic agent representing themselves on markets (which isn't true for many people, but sure let's go with it), then any equivalent system would have to factor in the amount of work they provide to the algorithms that are markets and provide an equivalent (alternatives might include surveys, bizarre computer generated questions, kickstarter style projects but with government/basic income style funds). That's fine, it's still an interesting direction of research, which would be necessary to understand the computational structure of economies.
The alternative claim, is that markets some how create a system that is greater than the sum of computers and people it encompasses... this paper deals with that by placing it squarely in the realm of NP completeness.