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My Research Scope and PurposeØ Purpose = Proposing landholding behavior empirical analysis framework
Landholding behavior

Travel behavior

Landowners’ data

Person trajectory data

Time series data = Trajectory data

Behavior Model

Model

Landholding pattern choiceLand transaction

Model

Sequential route choice1Land Transactions ModelØ Purpose : Propose a micro land-transportation interaction model consisting of three agentsLand selling choice modelLand Buying choice model① Agent: Seller② Agent: Buyer

Chooses tosell the set of plots 𝑖and keep the set of plots𝑖 !

Chooses to buy the plot j③Agent: Visitor

Visit Volume per Link from behavior survey

2Land Transactions ModelØ Consider interaction between selling and buying transaction

Land selling choice model𝑉{ / , / #}Trip volume term

= 𝜽%+,&& 𝑿{/}# + 𝛼+,&& ' 𝑄&&,/ #!∈("Attribute term"#$ ,+ 𝛾+,&& ' 𝛿&(𝜽1#$ )&,/! ∈("Land Buying choice model𝑉!

Trip volume term

= 𝜽%"#$ 𝑿! + 𝛼"#$ ' 𝑄&Attribute term

& !!∈(",-,&& )+ 𝛾"#$ ' 𝛿&+,&& (𝜽&,!! ∈ *Inference term

Inference term

Visit Volume per Link from behavior survey

3

Land Selling Choice Modell Deterministic term of utility functionl Choice behavior
Seller chooses to “sell the set of plots 𝑖and “keep the set of plots 𝑖 !

““𝑉{ $ , $ ! }Attribute term

Trip volume term

= 𝜽*'()) 𝑿{$}! + 𝛼'()) ' 𝑄)

l Choice set
Choice set is owned land combination.
Choice setChosen

11112222),$ ! " ∈,#Inference term+ 𝛾'()) '-./ ,𝛿) (𝜽0./ )),$" ∈,#- l refers to link
3 "#$ is estimates of the buy model- 𝜽- Parameter is 𝜽%&'' = (𝜽(&'' , 𝛼(&'' , 𝛾(&'' )4Land Buying Choice Modell Deterministic term of utility functionl Choice behavior
Buyer chooses to buy the plot j

𝑉:
Attribute terml Choice set
randomly sampled from sold land

Trip volume term

= 𝜽*-./ 𝑿: + 𝛼-./ ' 𝑄)
) :" ∈,#
Inference term,<()) )+ 𝛾-./ ' 𝛿)'()) (𝜽sold lands
Chosen),:" ∈ ;- l refers to link
3%&'' is estimates of the sell model- 𝜽- Parameter is 𝜽"#$ = (𝜽)#$ , 𝛼)#$ , 𝛾)#$ )5

Matching Algorithm: Summaryl Formulate matching of selling and buying using the estimation results ofa land transaction model.
l Using the estimation results, it is possible to determine the order ofpreference of the two economic agents, the seller and the buyer.
l Aim for “stable matching” by applying Gale-Shapley's DA algorithml Assume that the seller and the buyer are either in a state in which bothare not matched or in a state in which matching is tentatively
established6

Matching Algorithm: Detail
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 atentative 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 buyerare compared, and the buyer with the higher selection probability isprovisionally matched.
4. If the provisional matching with the seller is resolved, the buyer removes theresolved seller's land from his preference list and becomes free.
5. The above procedure is repeated until there are no more buyers who are nottentatively matched.

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Digitize Method for Real Estate Registration Data
Ø Two types of data converted for disaggregated and network datal Owner and land attributes for each lot number per year for disaggregated datal Transaction graph list for the clarification of transaction
List of Owner and Land Attributes“売買”Lot. NoYear

Name

1517-1

2004

Xxx, xxx

1517-1

2005

Mastuyama-shi

1517-1

2006

Mastuyama-shi

...

...

...

1517-2

2005

Mastuyama-shi

Traced Surveyed Map

combine{1000, 2005,Matsuyama-shi}

Transaction Graph

Fig. Real Estate Registration Data

Year

Seller

Buyer

2004

Xxx, xxx

Mastuyama-shi

...

...

...

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Case Study Area : Dōgo Onsen Districtl Dōgo held some major urban development in 2004-2009, 2013-2017.
l Both land-related and travel-related data exist.

2. Digitizing Method of Cadastre Data○○○●○

9Model Specification
Parameter

Variable Name

Description

Cluster Size（/10m）

Average distance from the center of gravity of clusters obtained byclustering already owned plot by Ward's method to the center of gravity ofmaintained/purchased plot polygons

Length of Frontage (/10m）

Average length of the plot boundary that intersects the perpendicular linefrom the center of gravity of the maintained/purchased plot polygon to theroad link. If the perpendicular line intersects another plot polygon, it isassumed to be 0m as it is not tangent to the road.

Volume of Visits

Number of visitors per link revealed by migratory behavior data𝛾(&''Estimated Selling Volume

Estimated sale volume per link calculated from the sold land choice model𝛾)#$

Estimated Buying Volume

Estimated purchases per link calculated from the purchased land choicemodel

𝜽2+,&& , 𝜽2"#$𝛼(&'' , 𝛼)#$10

Estimation Result
2009-2013
Sell
Buy-2.341-1.175-4.678**-4.130**2013-2017
Sell
Buy-0.528-0.894-6.240**-4.147**2017-2021
Sell
Buy-0.243-1.496-0.310-2.507**

Cluster SizeEst.
t-value

2004-2009Sell
Buy-1.974-0.684-5.184**-5.608**Length of Frontage

Est.
t-value

0.459
5.064**

0.382
3.505**

1.680
10.801**0.695
2.514**-3.8189.066**

1.047
3.001**

1.690
8.772**

0.381
1.751*

Volume of Visits

Est.
t-value

3.023
3.096**-0.306-0.5662.894
2.651**-0.737-0.4191.486
1.803*

4.183
0.632

2.127
2.440**-1.875-0.622Estimated
Buying VolumeEst.

-0.308--0.565-0.708--0.907-t-value-14.872**--10.714**--10.484**--8.760**-Est.
t-value--0.009-0.308--0.167-2.731**--0.063-0.916--0.026-0.322-1393.707-894.267
0.355
1717

-220.606-160.3070.269
92-1275.413-643.540
0.492
1607

-136.680-71.1660.472
57-980.078-508.008
0.478
1230

-122.293-83.9270.306
51-718.381-357.7480.496
884-100.712-66.255
0.332
42

Estimated
Selling Volume
LL(0)
LL
ρ2
Number of Sample

11

Estimation Result
2009-2013Sell
Buy-2.341-1.175-4.678**-4.130**2013-2017
Sell
Buy-0.528-0.894-6.240**-4.147**2017-2021
Sell
Buy-0.243-1.496-0.310-2.507**1.690
8.772**

Cluster Size

Est.
t-value

2004-2009Sell
Buy-1.974-0.684-5.184**-5.608**Length of Frontage

Est.
t-value

0.459
5.064**

0.382
3.505**

1.680
10.801**0.695
2.514**-3.8189.066**

Volume of Visits

Est.
t-value

3.023
3.096**-0.306-0.5662.894
2.651**-0.737-0.419Tendency
to maintain
1.486
4.183
2.127 high-1.875
1.803*
0.632
2.440**-0.622
visits plots.

Estimated
Buying VolumeEst.

-0.308--0.565-t-value-14.872**--10.714**-Est.
t-value--0.009-0.308--0.167-2.731**-1393.707-894.267
0.355
1717

-220.606-160.3070.269
92-1275.413-643.540
0.492
1607

-136.680-71.166
0.472
57

Estimated
Selling Volume
LL(0)
LL
ρ2
Number of Sample

0.708

1.047
3.001**--0.9072009-2013 shows buying-10.484**
behavior with
an-8.760**
eye onselling-0.063-0.3811.751*---0.916--0.026-0.322-980.078-508.008
0.478
1230

-122.293-83.9270.306
51-718.381-357.7480.496
884-100.712-66.255
0.332
4212

Estimation Result
2009-2013
Sell
Buy-2.341-1.175-4.678**-4.130**2013-2017
Sell
Buy-0.528-0.894-6.240**-4.147**2017-2021
Sell
Buy-0.243-1.496-0.310-2.507**1.680
10.801**0.695
2.514**-3.8189.066**

1.047
3.001**

1.690
8.772**

0.381
1.751*

1.486
1.803*

4.183
0.632

2.127
2.440**-1.875-0.6220.708--0.907--10.484**--8.760**---0.063-0.916--0.026-0.322-980.078-508.008
0.478
1230

-122.293-83.9270.306
51-718.381-357.7480.496
884-100.712-66.255
0.332
42

Cluster Size

Est.
t-value

2004-2009
Sell
Buy-1.974-0.684-5.184**-5.608**Length of Frontage

Est.
t-value

0.459
5.064**

Volume of Visits

Est.
t-value

Tendency
3.023
to-0.306
maintain2.894high visits-0.737
3.096** over-0.566
2.651**
volumes
all time
periods-0.419

Estimated
Buying Volume

Est.

Selling behavior predicts buying-14.872**-10.714**
behavior,
whereasbuyingbehaviordoes
not predict-0.009-0.167selling- behavior-0.308-2.731**t-value
Estimated
Selling Volume
LL(0)
LL
ρ2
Number of Sample

Est.
t-value-0.308-1393.707-894.267
0.355
1717

0.382
3.505**--220.606-160.3070.269
92-0.565-1275.413-643.540
0.4921607--136.680-71.166
0.472
57

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Matching Resultl 2004-2013 results are best matchedl 2013-2017 results show an overselling and an increase in unmatched links

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Conclusion and Future works
Conclusionl Modeling interaction of landowners by discrete choice modell Proposing the specific methods for efficient land matchingü Using DA algorithm and estimation results
ü Matching computation time was less than 0.1 second: practicalü Matching result shows seller’s dissatisfaction
Future worksl Seller’s dissatisfaction → Implementation of seller-proposed matching algorithml Introduction of indicators of matching efficiency
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