I recently went to a Christmas party where, instead of a gift exchange, there was a donation exchange. Essentially, we each placed a cause’s name into a hat, people draw the names and are asked to donate to the cause. You may donate any amount you wish (including nothing if you are particularly opposed to the cause you drew). Given that this a group of people that have collectively decided to opt for altruism, the honour system should work. As a result, I will be donating to the World Food Program and someone will be donating to Planned Parenthood on my behalf.
Someone at the party suggested that next year they hold a Yankee swap version where, rather than simply draw and donate, people may later “steal” causes by agreeing to donate more than the current donor. However, I thought this might be unfair to those attending who happen to be unemployed or wracking up student debt. I was wondering if there is an algorithmic-game-theory person out there who could come up with a way to deal with this that might meet the following conditions:
- the total amount donated is maximized (or at least the price of anarchy is bounded)
- each person ends up matched to a cause (that is not their own)
- each person can cap their donation according to their means
- one’s cap does not hinder the ability to steal a cause
- the game doesn’t take forever and the rules are simple enough for a smart crowd to understand
I suppose one could hide everything and have causes bid on like Google AdWords, but I think a game of stealing in the spirit of Christmas would be more fun.
Planned Parenthood info:
http://www.bbb.org/charity-reviews/national/human-services/planned-parenthood-federation-of-america-in-new-york-ny-626
Quality varies according to
http://www.charitynavigator.org/index.cfm?keyword_list=planned+parenthood&Submit2=GO&bay=search.results
World food program is good:it seems
http://www.bbb.org/charity-reviews/national/relief-and-development/friends-of-the-world-food-program-in-washington-dc-1612
see also the 4 stars at
http://www.charitynavigator.org/index.cfm?keyword_list=world+food+program&Submit2=GO&bay=search.results
I don’t think that we can put a bound on the price of anarchy in a traditional Yankee swap unless the ratio between the poorest person and the richest person is also bounded.
But you could perhaps devise a Yankee swap where people pay money to buy charities from one another after their initial free choice (the money paid to a person would, at the end of the game, so to the charity of their choice). In this way, a poor person with a good charity could get money to buy a charity they really wanted to help out, and a rich person could end up with the charity they really want – but for a price.
Now I want to formalize this model and see if it has any of the nice properties one might want, but must head off to class.
* the total amount donated is maximized (or at least the price of anarchy is bounded)
* each person ends up matched to a cause (that is not their own)
* each person can cap their donation according to their means
* one’s cap does not hinder the ability to steal a cause
* the game doesn’t take forever and the rules are simple enough for a smart crowd to understand
Intuitively there doesn’t seem to be anything here that would necessitate anyone paying under their cap. If you want to maximize amount donated, you should be able to get everyone up to their cap. For example: everyone randomly draws a charity other than their own, but then each person has the option to pay the person who picked their charity, to donate extra. “You don’t like the charity you drew, which I suggested? I’ll give you the difference between my cap and the amount I’m planning to pay for the charity I drew, if you agree to donate the same amount in addition to whatever you were planning.” If everybody makes this offer, as they clearly have an incentive to do, and everyone accepts this offer, which they might as well do since otherwise the offerer will probably just go home afterwards and donate that money themselves, then everyone spends fully according to their means, and everyone’s desires are maximally met.
Now, this game would probably not be fun, but it would meet the criteria you set out. And from a utilitarian perspective, if you’re trying to maximize donation, the whole “assigning people to charities that wouldn’t be their top choice” thing is pretty artificial/meaningless in the first place.
Which is not, of course, a criticism of Shannon’s game, as long as donation-maximization is not the point of the game. It seems like a great way to spark thought and debate, for example.
Nice idea. Actually, I have one paper about charity mechanisms and another about gift exchange games, but never thought of combining the two! Maybe there’s an interesting problem to define there.
The idea for the charity mechanism paper is to increase donations through matching games: there’s a single cause that people are considering donating to. each person decides about his/her cap, and then offers to match other people’s donations (e.g., for every dollar X donates, i’m willing to donate 10 cents). Given a collection of offers of this form, it’s possible to compute the maximal feasible set of payments. Furthermore, this algorithm defines a mechanism that has an efficient equilibrium (here efficiency is well defined and doesn’t involve everyone donating their maximum).
@Andrew: Here’s a utilitarian justification I can think of for an game like this: if you have a trusted charity A and I have a trusted charity B, and each of us wants to donate $100 to their charity, by swapping (I donate to your charity, you donate to mine), we don’t lose anything (each of us is donating the $100 we wanted to donate), but we gain information (in the form of both knowing that this charity is trusted by my friend, and also we might get some info about how our donations are spent), and this can lead to future donations.