Bunty, a close friend from school, got married yesterday in Hyderabad. There is a reception in Bangalore on Sunday. Given that he is the first person in our “gang” to get married, we are quite thrilled (and in a way scared). Of course, there is the small matter of a gift.
Now, there are six of us, in markedly different professions, and we think it would be nice if we could all pool in and buy a common gift for Bunty. Apart from me, there is an international lawyer, a dentist, a sub-editor of a tabloid, a developer at a huge IT services firm and yet another MBA.
The problem here is to determine the “budget”. Given that we are in vastly different professions, with vastly different salaries, this is not a trivial exercise. Prudence demands that all of pool in the same amount of money for the gift; the problem here is to determine this individual contribution.
One option would be for one of us to poll the rest of the members, find out each person’s willingness to pay (WTP) and fix the lowest WTP as the individual contribution. Sounds fair enough, since no one would be stretched beyond his/her means and still all of us would be contributing the same amount.
However, how can I be sure that everyone has mentioned their true WTP? I know that there is one person in the group who is still mainly living on her parents’ money. And I might want to quote a low WTP in order to not embarrass her. If everyone thinks the same, the final contribution might be much lower than everyone’s true WTP. Won’t be fair either to Bunty or for any of our consciences.
Rather, is there a way of selecting the person who conducts the “survey” (after all, all of us have a rough idea as to each others’ salaries) so that most people end up stating their true WTPs?
And is it better for us to conduct the survey in two rounds, where we announce everyone’s first round bids before soliciting the second round bids?
Also, will the problem get further complicated if only bilateral (rather than multilateral) communication is allowed? Like this evening, we were all coordinating through text messages – a bilateral channel.
Unfortunately we didn’t do any such thing this evening. We weren’t careful enough in polling, and ended up broadcasting our WTPs. Maybe a couple of us got a little upset, or embarrased. One of us proposed that it is ok if all of us contribute our individual WTPs (rather than equally) and buy the gift. Not a great idea, I realize now. Finally it was decided that it’s not that great an idea to pool in all the resources.
Now we have two sub-gift-committees. And yeah, the unenviable task lies ahead of selecting an appropriate gift for Bunty (now that we have fixed the budget). And it is proving to be a damn tough task. With only two days to go, time is also short. Hopefully we should come up with something nice.
Hi,
Nice post. Here’s my solution. Implementation hassles are there, but I guess the theory is sound.
N people – A1, A2, …, An; Each Ai corresponds to a particular person, and this is fixed, and everyone knows this.
Premise – To get to the fair solution, one must create a way for people to communicate their WTP in such a way that no one gets to know anybody else’s WTP. This is possible in my solution if people play by the rules.
Round 1
A1 takes a large random number, adds his WTP and passes the sum to A2. Every Ai adds his/her WTP to the number he/she receives and sends the sum to A(i+1). A1 finally receives the sum from An, subtracts his initial random no. and arrives at the average of WTPs quoted and broadcasts this to the group.
Subsequent Rounds
Same as before, except that each Ai adds LOWER(his/her WTP, previous round’s average)
The game stops when 2 consecutive rounds yield the same average.
Let me know your thoughts.
-Vijay
IIMB, PGP 2006-08