What are some of the best examples of these kinds of games?
I'm surprised by how unprofessional and arrogant Bush seems. We really don't live in a meritocracy, do we?
Corporations cannot exist without government. Of course there can be a revolution which replaces the government with an existing organization such as a corporation. But then that corporation becomes the government. It will need to be funded too. Currently corporations which are larger than many governments are funded only by voluntary participants, if you don't include government subsidies. So it is not difficult to imagine governments too being supported strictly by voluntary payments from 'customers'.
It seems too difficult to imagine an emotional circumstance which has not already been experienced by many people with good documentation. Setting the foundations for re-imagined social systems, on the other hand, seems to be the way to get the most meaningful data from a social science experiment. I would implement a system which has been designed from the ground up to most equitably fund governments. Then I would pay particular attention to how it both improves itself and crumbles into chaos. See 'this linked comment' for an example of such a system.
When I am bored and I have no access to distractions, then I try to keep my sanity by identifying and solving problems. I arrived at that particular idea about 20 years ago while working as a technician in a high speed automated process. By the way, I started doing that after I ran out of ideas for improving the job I was doing. Edit: I like your post which you linked. I will try to imagine a good contribution for it.