Is an Auction the Best Way to Solve the Roommate/Rent Dilemma?

(Photo: Matthew Jording)

We’ve blogged before about the very common roommate/rent dilemma — that is, how to fairly split rent among roommates given that different rooms have different features. A reader named Michael Jancsy writes in with an auction solution and a request for feedback:

I recently designed an auction website [called “The Rent Is Too Damn Fair”] to help friends split apartments … The auction works by allowing each roommate to bid on each room in an apartment, and then identifies the permutation of roommates to rooms with the largest consumer surplus (sum of all bids minus rent paid to landlord) to decide who should live in what room. Each person’s rent is then calculated by dividing the surplus evenly over the occupants, so that the difference between a person’s bid and the rent paid is the same for each person. 

It’s a pretty rudimentary design, but I hope it will be superior to the methods more commonly used, such as basing rent only on square footage. I am somewhat concerned, though, that it is not strategy-proof.

I believe what Michael means by “strategy-proof” is that some people will likely try to game the auction to their advantage. So: feel free to give him your general feedback but especially with an eye toward his model’s shortcomings.


Jim Crandall

The process of pricing of rooms could be seperated from whom gets the room. What f the person who has the highest bid also gets the first choice of room/price combination? I'm going to have to look so see if this just makes the game play in reverse - Bid high causing average bids to create low room prices.

zepplin

There's no such thing as a "strategy-proof" solution. I think the word "auction" is giving you a false impression of fairness.

Consider the simplest case of one seller, one buyer, and one good. Whether you use "auctionning" or "haggling", you can quickly find out whether the surplus is positive or negative, but there's no way to divide the surplus "fairly" as both sides have an incentive to lie about their true valuation in order to get a larger share of that surplus.

There's no real advantage to use auctions over negotiations in this simple case, whether the good is an apple, or the "difference between two rooms". They are both just methods at arriving at an efficient price (if that is indeed the goal, for other goals, see reserve price).

There are advantages to use auctions of course, like when the market is poorly known, there are too many participants to negotiate, or for the sake of transparency. This misleading sense of "fairness" probably comes from that last reason, to avoid back-door deals or corruption. In the case of renting, however, this is irrelevant since all deals are already transparent and there's no corruption. (Note that collusion is not corruption in this sense, nor is it prevented by auctions).

In short, "auction" is no magic bullet. Personally, I would use negotiations over auctions in the rental problem since discovering an efficient allocation is not difficult at all (almost any method allowing iterations will work) and auctions doesn't help with fairness, just gives the appearance of it.

If your new roommates are complete strangers, negotiating is a good way to get to know one another, and if it breaks down, you can always resort to an auction. If your new roommates are friends, this is a chance to make use of the existing trust to ask for true valuations and arrive at a fair distribution, building more trust in the process. Making it into a "game" simply makes it more socially acceptable to "game". (see freakonomics)

Of course, gaming negotiations and gaming auctions require different skill sets. So maybe there's a reason to use auctions after all ;)

Read more...

MeanOnSunday

The site is down right now so I can't check how it works, but I would think that each person's bids would be required to sum to the total rent. This avoids all of the simple gaming strategies mentioned in previous posts

Daniel

Like others have said, the problem is the ability to game the system to a low number. Eliminate that problem by having a requirement that the sum of a individuals bids be >/= the total rent, though people are allowed to go higher. That gets the cheapskate strategy out of the way. (People may still have some incentive to lie if they have sufficient beliefs about other bidders and try to game the system, but that's relatively minor.)

Useful site in theory, just needs to be tweaked to avoid the NE that seems like a bad result.

MW

Alternatively, you could *require* that each person's lowest bid be $0. You are bidding for how much extra you would be prepared to pay to avoid getting dumped with last choice of room. Now the maximum-excess room allocation ought to sum to less than the total rent, and the remainder of the rent is split equally between the tenants.

Possibly this will work for couples as well. For the purpose of allocating rooms and finding the maximum excess, they are one person. When the remainder gets split, they are two people. However I'm not sure this will be entirely fair - I think it will overcharge couples. Perhaps you need an agreed on two-way division of the rent between public and private spaces, where they count as two people for the split of public space rent and one for the split of private space rent. (Shared en suites complicate things even further.)

asantiago72

A few years ago i rented an appartment with two other roomates. We all were econ graduate students.

We divided the process in two parts.

First we agreed on fair rents, depending on the rooms available.
After that, we asigned each room randomly.

I'm aware that this mechanism doesn't necessarily maximise surplus, but it eleminates the incentive to hide your preferences to manipulate the auction.

My guess is that as long as all involved have similar incomes and if the rooms are not ridicously different, this mechanism results in a fair way to allocate rooms and rent.

At least we were happy with it.

Dr. Constantinos Charalambous

What is described as fair for one of the roommates may be unfair for another. Fairness is rather subjective but embedded in different degrees in our personality. See what happens in the following experiment when a monkey is given a cucumber.

http://www.everyday-economist.com/2012/09/what-happens-when-you-give-monkey.html

william

This basically gives people that don't care what room they get an unfair advantage.

I would just put $1 or whatever minimum there is for each room. Rent that cheap more then compensates for whatever shortcomings a room might have. I assume they all pass basic livability standards.

Michael Jancsy

Thank you everyone for your comments! There are many thoughtful and insightful contributions here, and we’ll be incorporating them into a more comprehensive FAQ in the coming weeks. Special thanks to Stephen Dubner and everyone at Freakonomics for generously helping TheRentIsTooDamnFair!

Evan

I did some work on this exact problem last year.
It turns out that it is impossible to find a solution that satisfies all four of the following reasonable conditions:
1. efficiency (in the sense that the solution must be pareto optimal)
2. envy-freeness of the final allocation (i.e. no one wants to swap with anyone else)
3. incentive compatibility (i.e. no one lies to try and game the system)
4. Budget balance (i.e. you collect enough money to pay the rent exactly)

The proof is via an application of the Groves-Clark mechanism.
Of the solutions that already exist in the literature, I prefer that of Azacis (2008, Games and Economic Behaviour). This solution relaxes condition 3. above (incentive compatibility), although the mechanism is fairly complex so that it would be very difficult for anyone to work out an optimal deviation from truth-telling.

Joshua

Actually I dealt with this by using the surplus solution (any extra is given back equally) and starting the bids for each room at 1/3 the rent (for three people). This guaranteed the minimum rent, and essentially turned it into who would pay a premium for what room. For example, rent of 900, the bidding on each room started at 300, and then assuming one person bid 100 extra for a particular room, he would pay 366 while the other two paid 267.

Mark

You definitely need to set a restriction on each roommates bids (eg total bids by each person must sum to total rent).

Other than that I quite like the idea you'll probably achieve close to the first best solution but since the amount you pay is some function of your bid it still means the optimal strategy is to bid differently your actual valuation leading to inefficiency (see Vicky Groves).

See alsp Myerson-Satterthwaite theorem for conditions where there is no way of implementing a satisfactory incentive compatible solution.

Andy

As other commenters have pointed out, this is strongly subject to being gamed. I suggest implementing a VCG auction, which avoids that problem.

S P

KISS! I think the SF method totally works... if you use the common space sf as split between every roommate and the bedroom sf as applying only to those who have that room. Total rent/total sf is the rent/sf used. In a $900 rent situation, with relatively equal bedrooms, and two people share one room and one person having the second to themselves, the rent would be about $350, $275, $275. And this is about right.

Ecomplicated

Why not just have the roommates bid on each room? The largest room goes to the person who will pay the most for it, and so forth to the worst room. If he/she wants the master bedroom so bad let em pay as much as they'd like and lower the rent for the others. A complicated formula/system is not needed to solve the roommate dilemma, just common sense. Another roommate tip, don't room with a$$holes who will bid $1 on a room.