3 ms·

0: Total rent is $10, for ten rooms, to be split among ten people. 1: One person who really wants a certain room bids $10 on it, and he assigns $0 to the nine

0: Total rent is $10, for ten rooms, to be split among ten people. 1: One person who really wants a certain room bids $10 on it, and he assigns $0 to the nine other rooms. His roommates bid a neutral $1 on all rooms. ... 4: The person gaming the system gets his special room. 5: The surplus is $10 + 9*$1 - $10 = $9. Split evenly, $0.90. Thus, the gamer pays $9.10 for his special room, and everyone else pays $0.10 for their rooms. He has clearly made a terrible mistake. He's covering the cost of the entire rental nearly by himself. Next time, he bids $1 + one gummy bear on his special room, and he bids $1 on the other rooms. He imagines that now he'll merely have to buy one gummy bear every month, split it in ten, and give everyone a slice. He's outwitted his roommates, he thinks. However, much to his dismay, he overlooked that one of the rooms in this next rental was underground. Furthermore, the room was next to a leaky sceptic tank. Everyone else bid $0 on it. The gamer handily wins the sewage room, instead of his special room, and he hardly gets any discount for putting up with it. Oops, foiled again. All of this is to say, your system seems robust. There's danger in over and underbidding on your assessment of a room's value. You want to be very careful in deciding how much a room is worth to you. I think I'll use this system for renting Airbnb's with friends in the future. Thanks!

mjevans 5y ago
Much like with underutilized amusement park rides, the system must accept 'negative' value on some queues (lost guest displacement time in that case) to correctly price the value of the desired outcomes. As far as the 'sewer room' option goes, I think it would have to be priced at the cost of renting somewhere else; so a negative value. For the split on the surplus rent there are a couple solutions to this. IIRC it might be a dutch auction rule? The one where if N of a thing are available a there are N winning bidders all the winning bidders pay the lowest price? Take that rule except apply it to the lowest choice total among the set that yields a full rent. There's also an argument about how to split the savings. In the 10 + 9 * 1 scenario the portion of the total rent the distribution of savings might be better split up as: 'refund' = SURPLUS * nROOM / (RENT + SURPLUS) nRENT = nROOM - SURPLUS * nROOM / (RENT + SURPLUS) If A = 10 and B..J are all 1 5.263... = aRENT = 10 - 9 * 10 / 19 0.526... = xRENT = 1 - 9 * 1 / 19 Rent (10) == A (5.26315789474) + Everyone else (4.73684210526) Even in the pathological case offered this works well enough.

mjevans 5y ago

Much like with underutilized amusement park rides, the system must accept 'negative' value on some queues (lost guest displacement time in that case) to correctly price the value of the desired outcomes. As far as the 'sewer room' option goes, I think it would have to be priced at the cost of renting somewhere else; so a negative value. For the split on the surplus rent there are a couple solutions to this. IIRC it might be a dutch auction rule? The one where if N of a thing are available a there are N winning bidders all the winning bidders pay the lowest price? Take that rule except apply it to the lowest choice total among the set that yields a full rent. There's also an argument about how to split the savings. In the 10 + 9 * 1 scenario the portion of the total rent the distribution of savings might be better split up as: 'refund' = SURPLUS * nROOM / (RENT + SURPLUS) nRENT = nROOM - SURPLUS * nROOM / (RENT + SURPLUS) If A = 10 and B..J are all 1 5.263... = aRENT = 10 - 9 * 10 / 19 0.526... = xRENT = 1 - 9 * 1 / 19 Rent (10) == A (5.26315789474) + Everyone else (4.73684210526) Even in the pathological case offered this works well enough.