25st Sep 2022行動モデル夏の学校Modeling and Case Study of Land Transaction Mechanism with Gale-Shapley Algorithm Risa Kobayashi Department of Civil Engineering School of Engineering, The University of Tokyo
▷ Purpose = Proposing landholding behavior empirical analysis framework Landholding behavior Landowners' data Time series data = Trajectory data Landholding pattern choice Land transaction Travel behavior Person trajectory data Model Sequential route choice 1
>  Purpose : Propose a micro land-transportation interaction model consisting of three agents Land selling choice model Chooses to sell the set of plots {i} and keep the set of plots {i}- Chooses to buy the plot j BAgent: Visitor Visit Volume per Link from behavior survey Land Buying choice model 21
▷ Consider interaction between selling and buying transaction Visit Volume per Link from behavior survey w

● Choice behavior
Seller chooses to “sell the set of plots {i}      “ and “keep the set of plots {i}−     “
● Choice set
Choice set is owned land  Combination.
Deterministic term_of utility function
V{{i},{i}-} I  refers to link Ô buy is estimates of the buy model Parameter is Osell = (Osell, Asell, Ysell) 4
● Choice behavior Buyer chooses to buy the plot j ● Choice set randomly sampled from sold land
Deterministic term of utility function
V j I   refers to link Ôsell is estimates of the sell model Parameter is θ buy = (θ buy, α buy, Y buy)
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● Formulate matching of selling and buying using the estimation results of a land transaction model. ● Using the estimation results, it is possible to determine the order of preference of the two economic agents, the seller and the buyer. ● Aim for “stable matching” by applying Gale-Shapley's DA algorithm ● Assume that the seller and the buyer are either in a state in which both are not matched or in a state in which matching is tentatively established
1. The free buyer makes an offer for the land with the highest probability of selection among his choices. 2. Next, if the seller who owns the land is free, he or she accepts the offer, and a tentative match is established. 3. If the seller who owns the land is already provisionally matched, the selection probabilities of the provisionally matched buyer and the newly offered buyer are compared, and the buyer with the higher selection probability is provisionally matched. 4. If the provisional matching with the seller is resolved, the buyer removes the resolved seller's land from his preference list and becomes free. 5. The above procedure is repeated until there are no more buyers who are not tentatively matched. 7
▷ Two types of data converted for disaggregated and network data ●  Owner and land attributes for each lot number per year for disaggregated data ● Transaction graph list for the clarification of transaction画
1517-2 2005 Transaction Graph
Fig. Real Estate Registration Data
● Dōgo held some major urban development in 2004-2009, 2013-2017. O Both land-related and travel-related data exist. Legends Project area ✿ Art exhibition locations Plot boundary Public bathing facilities Hotel Shopping street 150 200 m
O O O O

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●  2004-2013 results are best matched ●  2013-2017 results show an overselling and an increase in unmatched links

Conclusion
● Modeling interaction of landowners by discrete choice model ● Proposing the specific methods for efficient land matching ✓ Using DA algorithm and estimation results ✓ Matching computation time was less than 0.1 second: practical ✓ Matching result shows seller’s dissatisfaction
Future works
●  Seller's dissatisfaction → Implementation of seller-proposed matching algorithm ●   Introduction of indicators of matching efficiency