Mechanism Design-Based Mathematical Modeling of the Decoy Effect in Housing Type Selection

Sentot Eko Baskoro, I Nyoman Sutapa, Suhartono Suhartono

Abstract


This study develops a mechanism design-based mathematical model to induce a decoy effect in housing selection, shifting consumer preferences from small to large house types. Using an area-per-price utility function and dominance constraints, two optimal decoy configurations (adjacent and strong) are derived analytically. We consider a developer offering a small house (500,000,000 IDR; 40 m2 building; 100 m2 land) and a large house (1,000,000,000 IDR; 100 m2 building; 200 m2 land), and design an additional decoy alternative. By imposing dominance and feasibility constraints, we derive closed-form conditions on the decoy's building area Ad and land area Ld for two price levels, 750,000,000 IDR and 850,000,000 IDR. The resulting adjacent (Δ = 0.002) and strong (Δ = 0.010) decoys ensure that the large house weakly dominates the decoy while maintaining internal consistency of preferences. Sensitivity analysis shows that the advantage margin increases linearly with proximity and context intensity parameters. The proposed framework provides developers with an operational and auditable mechanism for housing portfolio design.


Keywords


attraction effect; asymmetric dominance; mechanism design; hous ing optimization; mathematical modeling

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References


[1] Markus Weinmann, Abhay Nath Mishra, Lena Franziska Kaiser, and Jan vom Brocke. “The attraction effect in crowdfunding”. Information Systems Research 34.3 (2022), pp. 1276–1295. DOI: https://doi.org/10.1287/isre.2022.1152.

[2] Geoffrey Castillo. “The attraction effect and its explanations”. Games and Economic Behavior 119 (2020), pp. 123–147. DOI: https://doi.org/10.1016/j.geb.2019.10.012.

[3] Simon P. Anderson and Levent Celik. “Product line design”. Journal of Economic Theory 157 (2015), pp. 517–526. DOI: https://doi.org/10.1016/j.jet.2015.01.014.

[4] Mark Armstrong. “Nonlinear pricing”. Annual Review of Economics 8 (2016), pp. 583–614. DOI: https://doi.org/10.1146/annurev-economics-080614-115650.

[5] Jeffrey Zabel. “The hedonic model and the housing cycle”. Regional Science and Urban Economics 54 (2015), pp. 74–86. DOI: https://doi.org/10.1016/j.regsciurbeco.2015.07.005.

[6] Cynthia dos Santos Hentschke, Patrícia André Tillmann, Carlos Torres Formoso, Vera Lúcia Milani Martins, and Márcia Elisa Soares Echeveste. “Using conjoint analysis to understand customer preferences in customized low-income housebuilding projects”. Ambiente Construído 20.1 (2020), pp. 247–262. DOI: https://doi.org/10.1590/S1678-86212020000100372.

[7] David Stenvall, Pontus Cerin, Bo Sjö, and Gazi Salah Uddin. “Does energy efficiency matter for prices of tenant-owned apartments?” Environmental Science and Pollution Research 29 (2022), pp. 66793–66807. DOI: https://doi.org/10.1007/s11356-022-20482-w.

[8] Igor Kaliszewski and Dmitrii Podkopaev. “Simple additive weighting—A metamodel for multiple criteria decision analysis methods”. Expert Systems with Applications 54 (2016), pp. 155–161. DOI: https://doi.org/10.1016/j.eswa.2016.01.042.

[9] Tatiana Dumbalska, Vincent Li, Konstantinos Tsetsos, and Christopher Summerfield. “A map of decoy influence in human multialternative choice”. Proceedings of the National Academy of Sciences 117.40 (2020), pp. 25169–25178. DOI: https://doi.org/10.1073/pnas.2005058117.

[10] Jie Liao, Yan Chen, Wen Lin, and Lin Mo. “The influence of distance between decoy and target on context effect: Attraction or repulsion?” Journal of Behavioral Decision Making 34.3 (2021), pp. 432–447. DOI: https://doi.org/10.1002/bdm.2220.

[11] Pranav K. Padamwar, Jagwinder Dawra, and Vishal K. Kalakbandi. “The impact of range extension on the attraction effect”. Journal of Business Research 126 (2021), pp. 565–577. DOI: https://doi.org/10.1016/j.jbusres.2019.12.017.

[12] Marius Usher, Konstantinos Tsetsos, Mark Glickman, and Nick Chater. “Selective Integration: An Attentional Theory of Choice Biases and Adaptive Choice”. Current Directions in Psychological Science 28.6 (2019), pp. 552–559. DOI: https://doi.org/10.1177/0963721419862277.

[13] Pelle Guldborg Hansen and Andreas M. Jespersen. “Nudge and the manipulation of choice”. European Journal of Risk Regulation 4.1 (2013), pp. 3–28. DOI: https://doi.org/10.1017/S1867299X00002762.

[14] Per Michaelsen. “Transparency and nudging: An overview and methodological critique of empirical investigations”. Behavioural Public Policy 8.4 (2024), pp. 807–817. DOI: https://doi.org/10.1017/bpp.2024.7.

[15] Till Grüne-Yanoff and Ralph Hertwig. “Nudge versus boost: How coherent are policy and theory?” Minds and Machines 26.2 (2016), pp. 149–183. DOI: https://doi.org/10.1007/s11023-015-9367-9.

[16] Eric J. Johnson et al. “Beyond nudges: Tools of a choice architecture”. Marketing Letters 23.2 (2012), pp. 487–504. DOI: https://doi.org/10.1007/s11002-012-9186-1.

[17] Stephane Hess, Andrew Daly, and Richard Batley. “Revisiting consistency with random utility maximisation: Theory and implications for practical work”. Theory and Decision 84.2 (2018), pp. 181–204. DOI: https://doi.org/10.1007/s11238-017-9651-7.

[18] Dana Naous and Christine Legner. “Leveraging market research techniques in IS: A review and framework of conjoint analysis studies in the IS discipline”. Communications of the Association for Information Systems 49 (2021). DOI: https://doi.org/10.17705/1CAIS.04906.

[19] Zukhra R. Gabidullina. “The problem of projecting the origin of Euclidean space onto the convex polyhedron”. Lobachevskii Journal of Mathematics 39.1 (2018), pp. 35–45. DOI: https://doi.org/10.1134/S1995080218010110.

[20] Marius S. Spektor, Sudeep Bhatia, and Sebastian Gluth. “The elusiveness of context effects in decision making”. Trends in Cognitive Sciences 25.10 (2021), pp. 843–854. DOI: https://doi.org/10.1016/j.tics.2021.07.011.

[21] Jakub Więckowski and Wojciech Sałabun. “Sensitivity analysis approaches in multi-criteria decision analysis: A systematic review”. Applied Soft Computing 148 (2023), p. 110915. DOI: https://doi.org/10.1016/j.asoc.2023.110915.

[22] Gökhan Demir, Prasenjit Chatterjee, and Dragan Pamucar. “Sensitivity analysis in multi-criteria decision making: A state-of-the-art research perspective using bibliometric analysis”. Expert Systems with Applications 237 (2024), p. 121660. DOI: https://doi.org/10.1016/j.eswa.2023.121660.

[23] Heinz H. Bauschke and Patrick L. Combettes. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. 2nd ed. Springer, 2017. DOI: https://doi.org/10.1007/978-3-319-48311-5.

[24] Markus Weinmann, Christoph Schneider, and Jan vom Brocke. “Digital nudging”. Business & Information Systems Engineering 58.6 (2016), pp. 433–436. DOI: https://doi.org/10.1007/s12599-016-0453-1.

[25] Karthik Ramakrishnan. “The Influence Of Decoy Pricing On Consumer Decision-Making: A Comprehensive Analysis”. International Journal of Computer Engineering and Technology 16.1 (2025), pp. 138–150. DOI: https://doi.org/10.34218/ijcet_16_01_013.




DOI: https://doi.org/10.18860/cauchy.v10i2.36937

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