Room Assignment A Market Approach Hassaan Khan and Sam Yellen Dec. 4, 2007

Room Assignment - The Status Quo Housing is a very stressful experience for undergraduates Residential Colleges divided into Suites which are comprised of rooms

Reasons for Stress Scarcity of Desirable suites Individual Preferences – Partners – Rooms Heterogeneous distribution Stickiness

Existing System 1.Form teams to enter “room draw” 2.Teams advised by rooming committee about availability 3.Each team draws a number 4.Teams choose suites, largest to smallest according to lottery number 5.Unsuccessful team broken up and redraw for a smaller room.

A Market Solution?

Why a Market Solution? Information asymmetry – Among groups – Within groups – Regulatory – (between housing committee and student body) Temporal Rigidity – If groups are awarded in a set order, certain behaviors are incentivized.

Markets Aggregate Preferences Information asymmetry – Price can signal preference For a individual choosing a group For groups choosing rooms Temporal Rigidity – Bids can be entered and modified simultaneously – Students can immediately bid on the rooms they find most desirable.

Market Design Each Student assigned 100 points. Scarcity of points forces bids to reflect preferences Two ways to bid – On individual room in a suite – Join a team and bid for a suite collectively Bidders can diversify the spending of their points, so that if they do not win a certain room they still have a chance to win a different room. Soft Ending – Auction closes a set amount of time after last bid.

Experimental Design 2 runs, 2 treatments each Each player assigned affinities for other players Status Quo vs. Market-Based Participants asked to team up with other players to maximize utility, the sum of affinities

Rooming in Residential Colleges There is enough housing for every student Rooms are grouped into suites

New Residential College President Levin announces the creation of a new residential college, Sunder College. Named after a professor who gave a very large donation. This college has 5 total suites, all rooms are singles – 1 quintet (r = 5) – 2 triples (r = 3) – 2 doubles (r = 2)

Lottery Treatment 1.Utilities Assigned 1.Partner Utilities 2.Form teams to enter “room draw” 3.Each team draws a number 4.Teams broken up and redraw for a smaller room.

Two Approaches Lottery Auction

Utility Maximization Total Utility = Who Who – Utilities Assigned to student ID’s

An Example 1.Two groups (G1 and G2) attempt to get a suite for 9 people. There is only one 9 person suite. 2.G1 draws a 5 and G2 draws a 10 3.G2 wins, G1 must break up and attempt to get a smaller room. 4.Process repeated for suites of size (9, 8, 7, 6, 5, 4, 3, 2).

Bidding System 1.Each Student assigned 100 points. 2.Two ways to bid 1.On individual room in a suite 2.Join a team and bid for a suite collectively 3.An example will be provided later 3.Bidders can diversify the spending of their points, so that if they do not win a certain room they still have a chance to win a different room. 4.Ending - last 30 seconds, bidders will be only able to change one bid.

Individual vs. Team bidding An example based on a double Z, with rooms Z1 and Z2 Bidder1 bids 20 on Z1 Bidder2 bids 30 on Z2 A team comprised of Bidder3 (bids 15) and Bidder4 (bids 40) bid a sum of 55 The team wins the suite

Individual vs. Team bidding cont. An example based on a double Z, with rooms Z1 and Z2 Bidder1 bids 20 on Z1 Bidder2 bids 30 on Z2 A team comprised of Bidder3 (bids 15) and Bidder4 (bids 30) bid a sum of 45 Bidder1 and Bidder2 win the rooms

Additional Instructions Don’t bid on 2 rooms in the same suite Restrain bidding activity in the final ending period. Partner Utilities – On a scale from -1 to 2 -1 : dislike 0: indifferent 1 : mild preference 2 : strong preference non mentioned utilities are assumed to be 0

Results Market and Status Quo outcomes Identical

Conclusions – Market Based Approach at least as efficient as status quo in allocating rooms. Other Observation: – Increased Utility of Larger rooms Larger groups can have more friends No additional preference for singles or smaller rooms

Problems Biased Group – groups sought to replicate success in previous round Order of treatments not reversed Suites were homogenous other than size Group too small Stickiness proportional to the number of possible groups In class, approximately 15 students taken 3 at a time = 455 possible combinations 200 students in groups of 5 – possible groups 7 orders of magnitude difference!

What do to next Redo Experiment – Same set of utilities but assigned to different students in each treatment – Increase Complexity Use a larger group of students Increase heterogeneity of rooms using floor maps Use homegrown affinities by letting groups of friends test the system. – Utility will be measured by using a questionnaire – Convince Pierson College to Accept Our System