Skip to main content
Log in

Solving House Allocation Problems with Risk-Averse Agents

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

This paper solves the fair and optimal house allocation problem (Sun and Yang, Econ Lett 81:73–79, 2003) when the agents preferences are represented by nonlinear utility functions using techniques for global mixed integer nonlinear optimization. A small simulation study indicates that if quasi-linear specifications are adopted as approximations to nonlinear utility functions and if the fair and optimal allocation is identified based on this approximation, then the prices are typically higher on average and the resulting allocation is typically non-fair.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adjiman C.S., Androulakis I.P., Floudas C.A. (1998a) A global optimization method, αBB, for general twice-differentiable NLPs—II. Implementation and computational results. Computers and Chemical Engineering 22: 1159–1178

    Article  Google Scholar 

  • Adjiman C.S., Dallwig S., Floudas C.A., Neumaier A. (1998b) A global optimization method, αBB, for general twice-differentiable NLPs—I. Theoretical advances. Computers and Chemical Engineering 22: 1137–1158

    Google Scholar 

  • Adjiman, C. S., Schweiger, C. A., & Floudas, C. A. (1998c). Mixed-integer nonlinear optimization in process synthesis. Handbook of combinatorial optimization, vol. 1. Kluwer Academic Publishers.

  • Adjiman C.S., Androulakis I.P., Floudas C.A. (2000) Global optimization of mixed-integer nonlinear problems. AIChE Journal 46: 1769–1797

    Article  Google Scholar 

  • Alkan A., Demange G., Gale D. (1991) Fair allocation of indivisible goods and criteria of justice. Econometrica 59: 1023–1039

    Article  Google Scholar 

  • Andersson T. (2007) An algorithm for identifying fair and optimal allocations. Economics Letters 96: 337–342

    Article  Google Scholar 

  • Andersson T., Svensson L.-G. (2008) Non-manipulable assignment of individuals to positions revisited. Mathematical Social Sciences 56: 350–354

    Article  Google Scholar 

  • Aragones E. (1995) A derivation of the money Rawlsian solution. Social Choice and Welfare 12: 267–276

    Article  Google Scholar 

  • Bussieck M.R., Drud A.S., Meeraus A. (2003) MINLPLib—a collection of test models for mixed-integer nonlinear programming. INFORMS Journal on Computing 15(1): 114–119

    Article  Google Scholar 

  • Chaudhuri A. (1986) Some implications of an intensity measure of envy. Social Choice and Welfare 3: 255–270

    Article  Google Scholar 

  • Crawford V., Knoer E. (1981) Job matching with heterogeneous firms and workers. Econometrica 49: 437–450

    Article  Google Scholar 

  • Deltas G. (2004) Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions. Economic Theory 23: 715–738

    Article  Google Scholar 

  • Demange G., Gale D. (1985) The strategy structure of two-sided matching markets. Econometrica 53: 873–888

    Article  Google Scholar 

  • Demange G., Gale D., Sotomayor M. (1986) Multi-item auctions. Journal of Political Economy 94: 863–872

    Article  Google Scholar 

  • Grossman, I. E. (2002). Review of nonlinear mixed-integer and disjunctive programming techniques. Optimization and Engineering, 227–252.

  • Gupta O.K., Ravindran A. (1985) Branch and bound experiments in convex nonlinear integer programming. Managment Science 31(12): 1533–1546

    Article  Google Scholar 

  • Haake C.J., Raith M.G., Su F.E. (2002) Bidding for envy-freeness: A procedural approach to the n-player fair division problems. Social Choice and Welfare 19: 723–749

    Article  Google Scholar 

  • Klijn F. (2000) An algorithm for envy-free allocations in an economy with indivisible objects and money. Social Choice and Welfare 17: 201–216

    Article  Google Scholar 

  • Kuhn H. (1955) The Hungarian method for the assignment Problem. Naval Research Logistics Quarterly 2: 83–97

    Article  Google Scholar 

  • Maskin, E. (1987). On the fair allocation of indivisible goods. In G. Feiwell (Ed.), Arrow and the foundations of the theory of public policy (pp. 343–349). MacMillan Press.

  • Shioura A., Sun N., Yang Z. (2006) Efficient strategy proof allocation algorithms. Journal of the Operations Research 49: 144–150

    Google Scholar 

  • Sun N., Yang Z. (2003) A general strategy proof fair allocation mechanism. Economics Letters 81: 73–79

    Article  Google Scholar 

  • Svensson L.-G. (1983) Large indivisibles: An analysis with respect to price equilibrium and fairness. Econometrica 51: 939–954

    Article  Google Scholar 

  • Tadenuma K., Thomson W. (1991) No-envy and consistency in economies with indivisible goods. Econometrica 59: 1755–1767

    Article  Google Scholar 

  • Williams H.P., Yan H. (2001) Representations of the all_different predicate of constraint satisfaction in integer programming. INFORMS Journal on Computing 13(2): 96–103

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tommy Andersson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andersson, T., Andersson, C. Solving House Allocation Problems with Risk-Averse Agents. Comput Econ 33, 389–401 (2009). https://doi.org/10.1007/s10614-008-9166-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-008-9166-y

Keywords

Navigation