Theory combining properties of auctions and charity matching - What strategy?
An auction works by driving up the price a small amount per bid. Strategic players will never bid more than they think the item is worth, but they can also expect to not bid much below that and still win.
"Charity matching" is a different game in how 2 players can drive up eachother's bids/payments by committing to pay, toward a common goal, at least what the other has paid. The return on investment as seen by each player is 2 times what it would be without such an agreement. But still there is the "common goal" part limiting what can be accomplished.
Even stranger than auctions or charity matching, consider what would be the best strategy in the following situations...
A man in a crowded area sets up a large timer and starts laying dollars on the ground and speaks loudly that whoever lays the last dollar on the pile, after nobody has laid any money for 1 minute, gets the whole pile. People may not believe him at first, but those who eventually see the game is playing by its own rules see their marginal-profit changing sharply just before the minute is up. Do they lay another dollar?
The dollars pile timer game is zero-sum, but the next one is positive-sum and is the important subject I'm asking about...
Someone finds 2
http://kickstarter.com (a charity funding platform) projects which have similar time ranges, funding so far about half way to their goal, total funding goals, and that this person would like to see both succeed at minimal cost to himself. From this we know the motivations of some people who have donated to those 2 projects, but is there a better way than "charity matching"? This may be... This person annouces to the world, and backs it up by paying this way over time which everyone can see, that whichever of those 2 kickstarter projects has the least total funding at a random time each day, this person donates a certain amount, which is enough to get public attention on their statement to the world about it and form strategies based on it. Wait, the least funded so far? Why do that? The people who tend to donate to those 2 projects would become in competition to be the least funded at every moment in time, in proportion to that "certain amount" donated per day. They would start donating to the opposite of the one they actually wanted to donate to so the other (which they prefer) would get the "certain amount" that day. Here's where it gets very self referencing... Knowing others will do that, they predict eachother, and each adjustment to those predictions of predictions of predictions... drives up 1 or the other project's total funding, while the extra payments per day pushes them toward equal total funding where this competition continues.
Regardless of if its charity or gambling or whatever form of greed, I'm talking about a system where everyone can see the total so far of these various accounts, and I ask... What is the best strategy? Is it to attempt to get the extra payment on your preferred target by funding its opposite, and let that accelerate upwards? Or is it to only do that to some proportion of the extra payment per day?
Consider what would happen if someone chose 100 kickstarter projects near equally valuable and similar to eachother's amounts and times like the one above. If someone was to apply this payment to the least funded one once per day at a random time, what would be the best strategy? I'm thinking it would be to view each as itself vs "all others", so still like 2 of them, but if everyone sees it that way, doeIf it change things?
Or much more abstract and simpler... A theory of economics in a simple game... N players each choose left or right each round, and whichever of left or right gets the least votes is the winning side, paid by the losing side (who voted the majority way). Doesn't that motivate them to predict eachother recursively? In the examples above with kickstarter, I'm talking about applying an economic force to the prediction itself instead of the money. I dont know how else to explain it.
There are so many possible ways to motivate people, its wasteful to act alone. But what is the theoretical limit of how much motivation can be amplified by any possible system of agreements?
