Journal of Statistical Theory and Practice

, Volume 7, Issue 3, pp 596–609 | Cite as

An Optimal Strategy for Maximizing the Expected Real-Estate Selling Price: Accept or Reject an Offer?

  • Martín EgozcueEmail author
  • Luis Fuentes García
  • Ričardas Zitikis


Motivated by a real-life situation, we put forward a model and then derive an optimal strategy that maximizes the expected real-estate selling price when one of the only two remaining buyers has already made an offer but the other one has yet to make an offer. Since the seller is not sure whether the other buyer would make a lower or higher offer, and given no recall, the seller needs a strategy to decide whether to accept or reject the first-come offer. The herein derived optimal seller’s strategy, which maximizes the expected selling price, is illustrated under several scenarios, such as independent and dependent offers by the two buyers, and for several parametric price distributions.


Real estate Optimal strategy Decision theory Uncertainty Two-envelope problem 


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  1. Albright, S. C. 1977. A Bayesian approach to a generalized house selling problem. Manage. Sci., 24, 432–440.CrossRefGoogle Scholar
  2. Anglin, P. M. 2004. How long does it take to buy one house and sell another? J. Housing Econ., 13, 87–100.CrossRefGoogle Scholar
  3. Anglin, P. M., R. Rutherford, and T. M. Springer. 2003. The trade-off between the selling price of residential properties and time-on-the-market: the impact of price setting. J. Real Estate Finance Econ., 26, 95–111.CrossRefGoogle Scholar
  4. Arnold, M. A. 1999. Search, bargaining and optimal asking prices. Real Estate Econ., 27, 453–481.MathSciNetCrossRefGoogle Scholar
  5. Biswas, T., and J. McHardy. 2007. Asking price and price discounts: The strategy of selling an asset under price uncertainty. Theory Decision, 62, 281–301.MathSciNetCrossRefGoogle Scholar
  6. Brint, A. 2009. Predicting a house’s selling price through inflating its previous selling price. J. Operational Res. Soc., 60, 339–347.CrossRefGoogle Scholar
  7. Cheng, P., L. Lin, and Y. Liu. 2008. A model of time-on-market and real estate price under sequential search with recall. Real Estate Econ., 36, 813–843.CrossRefGoogle Scholar
  8. DeGroot, M. H. 1970. Optimal statistical decisions. New York, McGraw-Hill.zbMATHGoogle Scholar
  9. Deng, Y., S. A. Gabriel, K. G. Nishimura, and D. Zheng. 2012. Optimal pricing strategy in the case of price dispersion: new evidence from the Tokyo housing market. Real Estate Econ., 40, S234–S272.CrossRefGoogle Scholar
  10. Denuit, M., J. Dhaene, M. Goovaerts, and R. Kaas. 2005. Actuarial theory for dependent risks: Measures, orders and models. Chichester, UK, Wiley.CrossRefGoogle Scholar
  11. Egozcue, M., L. Fuentes Garcia, W. K. Wong, and R. Zitikis. 2011. The covariance sign of transformed random variables with applications to economics and finance. IMA J. Manage. Math., 22, 291–300.MathSciNetCrossRefGoogle Scholar
  12. Furman, E., and R. Zitikis. 2008. Weighted premium calculation principles. Insurance Math. Econ., 42, 459–465.MathSciNetCrossRefGoogle Scholar
  13. Gastwirth, J. L. 1976. On probabilistic models of consumer search for information. Q. J. Econ., 90, 38–50.CrossRefGoogle Scholar
  14. Glower, M., D. R. Haurin, and P. H. Hendershott. 1998. Selling time and selling price: The influence of investor motivation. Real Estate Econ., 26, 719–740.CrossRefGoogle Scholar
  15. Horowitz, J. L. 1992. The role of the list price in housing markets: theory and an econometric model. J. Appl. Econ., 7, 115–129.CrossRefGoogle Scholar
  16. Jares, T. E., J. E. Larsen, and T. S. Zorn. 2000. An optimal incentive system for real estate agents. J. Real Estate Res., 20, 49–59.Google Scholar
  17. Larsen, J. E., and W. J. Park. 1989. Non-uniform percentage brokerage commissions and real estate market performance. J. Am. Real Estate Urban Econ. Assoc., 17, 422–438.CrossRefGoogle Scholar
  18. Lehmann, E. L. 1966. Some concepts of dependence. Ann. Math. Stat., 37, 1137–1153.MathSciNetCrossRefGoogle Scholar
  19. Lippman, S. A., and J. J. McCall. 1976. The economics of job search: A survey. Econ. Inquiry, 14, 155–189.CrossRefGoogle Scholar
  20. Mazalov, V. V., and V. Saario. 2002. The house-selling problem with reward rate criterion. J. App. Probability, 39, 644–649.MathSciNetCrossRefGoogle Scholar
  21. McDonnell, M. D., and D. Abbott. 2009. Randomized switching in the two-envelope problem. Proc. R. Soc. A, 465, 3309–3322.MathSciNetCrossRefGoogle Scholar
  22. McDonnell, M. D., A. J. Grant, I. Land, B. N. Vellambi, D. Abbott, and K. Lever. 2011. Gain from the two-envelope problem via information asymmetry: On the suboptimality of randomized switching. Proc. R. Soc. A, 467, 2825–2851.MathSciNetCrossRefGoogle Scholar
  23. Miceli, T. J. 1989. The optimal duration of real estate listing contracts. J. Am. Real Estate Urban Econ. Associ., 17, 267–277.CrossRefGoogle Scholar
  24. Nelson, P. 1970. Information and consumer behavior. J. Polit. Econ., 78, 311–329.CrossRefGoogle Scholar
  25. Ohnishi, T., T. Mizuno, C. Shimizu, and T. Watanabe. 2011. The evolution of house price distribution. RIETI discussion paper, Series 11-E-019.Google Scholar
  26. Read, C. 1988. Price strategies for idiosyncratic goods—the case of housing. J. Am. Real Estate Urban Econ. Assoc., 16, 379–395.CrossRefGoogle Scholar
  27. Riley, J., and R. Zeckhauser. 1983. Optimal selling strategies: When to haggle, when to hold firm. Q. J. Econ., 98, 267–289.CrossRefGoogle Scholar
  28. Rosenfield, D. B., R. D. Shapiro, and D. A. Butler. 1983. Optimal strategies for selling an asset. Manage. Sci., 29, 1051–1061.CrossRefGoogle Scholar
  29. Salant, S. W. 1991. For sale by owner: When to use a broker and how to price the house. J. Real Estate Finance Econ., 4, 157–173.CrossRefGoogle Scholar
  30. Sirmans, C. F., G. K. Turnbull, and J. Dombrow. 1995. Quick house sales: Investor mistake or luck? J. Housing Econ., 4, 230–243.CrossRefGoogle Scholar
  31. Stigler, G. J. 1961. The economics of information. J. Polit. Econ., 69, 213–225.CrossRefGoogle Scholar
  32. Yavas, A., and S. Yang. 1995. The strategic role of listing price in marketing real estate: theory and evidence. Real Estate Econ., 23, 347–368.CrossRefGoogle Scholar
  33. Zorn, T. S., and J. E. Larsen. 1986. The incentive effects of flat-fee and percentage commissions for real estate brokers. J. Am. Real Estate Urban Econo. Assoc., 14, 24–47.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  • Martín Egozcue
    • 1
    • 2
    Email author
  • Luis Fuentes García
    • 3
  • Ričardas Zitikis
    • 4
  1. 1.Facultad de Ciencias SocialesUniversidad de la República, UruguayMontevideoUruguay
  2. 2.Accounting and Finance DepartmentNorte ConstruccionesPunta del Este, MaldonadoUruguay
  3. 3.Departamento de Métodos Matemáticos e de RepresentaciónUniversidade da CoruñaA CoruñaSpain
  4. 4.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada

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