The method for the land plot value appraisal as part of the single real estate object, based on game theory approach
Abstract
In mass real estate valuation, in cadastral valuation, there is a problem of splitting the value of a single real estate object into the value of land plot and buildings (improvements) located on it. One of the key information sources for real estate valuation is market data. Such data may contain information on offer prices, as well as actual transaction prices (for example, in mortgage transactions) for the whole object. At the same time, in the accounting policy of enterprises different rates of land and property tax often require separate accounting of the value of land plots and the buildings located on them. The problem of such splitting of a single object’s value is the subject of permanent discussions in the valuation community. There are no established methods. This article proposes a method of splitting the value of a single property object based on the approach borrowed from co-operative game theory. A simple game formulation of the problem and its fair solution based on the Shepley value are considered. Simple and well-interpretable computational formulas are obtained, which allow us to split the market value of single objects on large data sets in minimum time. The proposed method is new in the theory and practice of valuation.
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References
Kuznetsov D.D., Myagkov V.N. (2023) Land – separately, building – separately. How to solve the problem of unfolding the market value of the pledged object. Bank Lending, no. 6(112), pp. 60–76 (in Russian).
Bure V.M., Staroverova K.Yu. (2019) Applying cooperative games with coalition structure for data clustering. Automation and Remote Control, vol. 80, no. 8, pp. 1541–1551.
Rozemberczki B., Watson L., Bayer P., et al. (2022) The Shapley value in machine learning. arXiv:2202.05594v2. https://doi.org/10.48550/arXiv.2202.05594
Roth J., Bajorath J. (2024) Machine learning models with distinct Shapley value explanations decouple feature attribution and interpretation for chemical compound predictions. Cell Reports Physical Science, vol. 5, no. 8, pp. 102–110. https://doi.org/10.1016/j.xcrp.2024.102110
Li M., Sun H., Huang Y., Chen H. (2024) Shapley value: from cooperative game to explainable artificial intelligence. Autonomous Intelligent Systems, vol. 4, article 2. https://doi.org/10.1007/s43684-023-00060-8
Feretzakis G., Sakagianni A., Anastasiou A., et al. (2024) Integrating Shapley values into machine learning techniques for enhanced predictions of hospital admissions. Applied Sciences, vol. 14(13), article 5925. https://doi.org/10.3390/app14135925
Kjersti A., Jullum M., Loland A. (2020) Explaining individual predictions when features are depended: More accurate approximations to Shapley values. arXiv:1903.10464v3. https://doi.org/10.48550/arXiv.1903.10464
Mikheenko A.M., Savich D.S. (2020) Application of Shepley value in regression analysis. Vestnik of I. Kant Baltic Federal University. Ser.: Physic-mathematical and technical sciences, no. 2, pp. 84–94 (in Russian).
Lundberg S.M., Allen P.G. (2017) A unified approach to interpreting model predictions. ArXiv:1705.07874v2. https://doi.org/10.48550/arXiv.1705.07874
Özdilek Ü. (2020) Land and building separation based on Shapley values. Palgrave Communications, vol. 6, article 68. https://doi.org/10.1057/s41599-020-0444-1
Petrosyan L.A., Zenkevich N.A., Semina E.A. (1998) Game Theory. Moscow: Higher School (in Russian).
Mazalov V.V. (2010) Mathematical theory of games and applications. St. Petersburg–Moscow–Krasnodar: Lan (in Russian).
Rusakov O., Laskin M., Jaksumbaeva O. (2016) Pricing in the real estate market as a stochastic limit. Log Normal approximation. International Journal of the Mathematical models and methods in applied sciences, vol. 10, pp. 229–236.
Aitchinson J., Brown J.A.C. (1963) The Lognormal distribution with special references to its uses in economics. Cambridge: University Press.
Ohnishi T., Mizuno T., Shimizu C., Watanabe T. (2011) On the evolution of the house price distribution. Understanding Inflation Dynamics of the Japanese Economy, Working Paper Series no. 56.
Laskin M.B. (2017) Adjustment of the market value by the pricing factor ‘area of the object’. Property relations in the Russian Federation, no. 8(191), pp. 86–99 (in Russian).
Rosreestr Order No. N/0336 dated 08/04/2021 (as amended on 09/11/2024) "On Approval of Methodological Guidelines on State Cadastral Valuation" (Registered with the Ministry of Justice of Russia on 12/17/2021 N 66421). Available at: https://www.consultant.ru/document/cons_doc_LAW_403900/ (accessed 30 January 2025) (in Russian).
Kabakov P. (2014) R in action. Data analysis and visualization in the R language. Moscow: DMK-Press (in Russian).
Zaryadov I.S. (2010) Introduction to statistical package R: types of variables, data structures, reading and writing information, graphics. Moscow: PUDN Publishing House (in Russian).
Feller W. (1971) An introduction to probability theory and its applications, vol. 2. John Wiley & Sons; 2nd edition.
Korkmaz S., Goksuluk D., Zararsiz G. (2014) MVN: An R package for assessing multivariate normality. The R Journal, vol. 6(2), pp. 151–162. https://doi.org/10.32614/RJ-2014-031
Korkmaz S., Goksuluk D., Zararsiz G. (2019) MVN: An R package for assessing multivariate normality. Trakya University, Faculty of Medicine, Department of Biostatistics, Edirne, TURKEY, MVN version 5.8 (Last revision 2019-09-27). Available at: https://cran.r-project.org/web/packages/MVN/vignettes/MVN.pdf (accessed 30 January 2025).
Puzynya N.Y. (2020) Modern market trends and market value assessment: collective monograph. St. Petersburg: Izd-vo Sankt-Peterburgskogo universiteta (in Russian).
Barinov N.P. (2022) Application of regression analysis methods in the tasks of individual and mass valuation of real estate objects. Valuation Issues, no. 1(106), pp. 34–46 (in Russian).
Anisimova I.N., Barinov N.P., Gribovsky S.V. (2004) Accounting for different types of price-forming factors in multidimensional models of real estate valuation. Valuation Issues, no. 2, pp. 2–15 (in Russian).
Barinov N.P. (2019) Calculation of the uncertainty interval of value estimation by methods of the comparative approach. Valuation Issues, no. 4(98), pp. 2–10 (in Russian).
