Game Theoretical Frameworks to Determine Rent Allocation Among Roommates Game Theory Among Friends MBA 211 Game Theory Final Project, Professor John Morgan The Stalemates: Chris Finegold, Jed Hwang, Phil Seo, Sheil Tamboli, Jia Jia Ye 5/13/2010 1 SITUATION OVERVIEW Many Americans have had the experience of living with roommates before marriage. At Haas, living with roommates is the norm: 85% of students live with one or more roommates and 28% live with two or more roommates1. During the housing group formation, there is always a point in which the roommates must decide on allocation of the rooms and the pricing split between those rooms. Sometimes, this is very simple – a house with equal sized rooms often is split equally among all roommates – but sometimes this can become significantly more complicated when a house has heterogeneous rooms and different demand for each room. There are often awkward, light‐footed discussions around the selection and pricing, as each roommate hopes to secure a good deal for himself without appearing to have a self‐interested motive for the sake of social unity. We believe this can lead to a suboptimal outcome, and that game theory can be used to help the roommates come to a happy equilibrium solution. In this paper, we examine in depth one scenario of five potential roommates who hope to share one house and apply our proposed game theoretic solution. The House A group of four girls found one house they all loved: a large, beautifully‐furnished, well‐located house that was owned by Asian antique art dealers who were currently traveling in Asia. However, the 4‐bedroom, 2 bathroom, 2 half‐bathroom house was priced at $5,000 a month, and that was more than the girls could afford. The girls, however, were desperate not to give up on the house, with its Steinway grand piano and convection ovens, and recruited a fifth girl to join in the fun. 1 Days at Haas Student and Housing Panel, May 1, 2010 2 While the house had four official bedrooms, the girls agreed that there was potential to convert the master bedroom and its sitting room into two separate rooms. They agreed that at an average price of $1,000 per person per month, each girl was comfortable with moving ahead with the lease‐signing, and that they would decide the final room allocations over the next few weeks. The “five” rooms that were created had significantly different qualities, and the girls each thought through which room they wanted. The Master: Although the original master bedroom was going to be split into two rooms, the inner room was still considered the Master Bedroom. It was the second largest room in the house with east facing windows and an entire wall of closet space. The room came furnished with a king‐sized bed and an antique dressing mirror. There was no private balcony and no views, but easy access to stairs that led to the backyard. The Walk‐Through: The original master bedroom had a sitting bedroom, which the girls converted into the Walk‐Through Bedroom. The room was only slightly smaller than the Master Bedroom and had its own clothing closet. In addition, the Walk‐Through had a built‐in entertainment center with a 40‐inch flat screen TV. However, the Walk‐Through lacked privacy since one had to cut through the corner of Master bedroom Walk‐Through The Master BedroomThe Walk‐Through BedroomMaster bathroomClo setClo set3 the Walk‐Through to enter the Master, and since it shared a common wall with the bathroom, shared by the Master and the Walk‐Through. The Twins: The twins were two small rooms that mirrored each other in size and quality. Both had wall‐length closets, and both had private balconies. They were nearly identical except that Twin #1 had a better view and Twin #2 shared a wall with the hallway bathroom. The Treehouse: In the attic was the Treehouse. It was the largest room of the house and had tons of light, brand‐new full carpet, and a unique charm. However, the ceiling sloped on both sides of the room, making it uncomfortable for anyone who was tall or claustrophobic. In addition, the attic would get the hottest during the summer and whoever lived there had the added responsibility of chasing out squirrels that would sometimes climb through the windows when open. While there was no real balcony, there was easy access to the rooftop which one could relax on. And finally, there was no closet in the Treehouse. The Twins and the Treehouse all shared the same hallway bathroom. Twin #1 Twin #2Twin #1 closetTwin #2 closetBalconyBalconyTwin #2 The Treehouse 4 The Girls The girls living in the house were similarly heterogeneous and diverse in their preferences and requirements. Three were under 5’ 3” and could easily fit into the Treehouse, two were in some stage of a relationship and needed more privacy than the Walk‐Through provided, and two were sensitive to cost. Most held similar waking hours, with one extreme early bird and no extreme night‐owls. In addition to these individual requirements, the girls were also at varying levels of friendship and comfort with each other, and this discrimination was revealed through bidding disparities and altered willingness to pay when certain pairs were matched for the Walk‐Through/Master combo. A summary of the girls is described below. Jia Jia Tina Elise Abi Siddhi Relationship Single Semi‐relationship (local) Single Single Long‐distance relationship Financial Flexible Flexible Price‐sensitive Flexible Price‐sensitive Current rent (pre‐Arch St.) $750 $1,000 $850 $1,200 $1,000 Height 5’ 3” 5’ 3” 5’ 6” 5’ 8” 5’ 1” Other Can be stubborn Focused on household harmony 5th roommate Most polite Concerned with delta in room costs While most girls preferred either the Master or the Twin rooms, Tina and Elise appeared to be most open of the five girls to the possibility of living in either the Treehouse or Walk‐Through. 5 THE ORIGINAL AUCTION The