# Satisfied two-sided matching: a method considering elation and disappointment of agents

- 374 Downloads
- 5 Citations

## Abstract

In practical two-sided matching problems, every agent usually cares about the matching result. If the result reaches or exceeds his/her expectation, he/she will experience elation; otherwise, he/she will experience disappointment. This is the psychological behavior of agents in two-sided matching, and the satisfaction degrees to the potential matching result of agents are closely related to the psychological behavior. However, the psychological behavior of agents is missing in the existing two-sided matching methods. The purpose of this paper is to develop a method for the two-sided matching problem considering psychological behavior of agents on both sides. First, the expected preference ordinals of each agent toward opposite agents are calculated based on the uncertain preference ordinals provided by agents. Then, the preference utility function is constructed, and the expected preference ordinals are transformed into preference utility values using the preference utility function. Next, based on the disappointment theory, the modified preference utility values are determined by calculating the disappointment values and elation values of each agent to the possible matching results. Furthermore, to maximize the sum of modified preference utility values of all agents on each side, a bi-objective optimization model is constructed, and the satisfied matching result can be obtained by solving the optimization model. Finally, a numerical example is used to illustrate the use of the proposed method.

## Keywords

Two-sided matching Uncertain preference ordinal Psychological behavior Disappointment Elation Optimization model## Notes

### Acknowledgements

This work was partly supported by the National Science Foundation of China (Project Nos. 71571039 and 71401131), Humanities and Social Science Foundation of Ministry of Education of China (Project No. 14YJC630063), Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2016JM7002) and the 111 Project (B16009).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical standard

This article does not contain any studies with human participants or animals performed by any of the authors.

## References

- Azevedo EM (2014) Imperfect competition in two-sided matching markets. Games Econ Behav 83:207–223MathSciNetzbMATHCrossRefGoogle Scholar
- Bell DE (1985) Disappointment in decision making under uncertainty. Oper Res 33(1):1–27MathSciNetzbMATHCrossRefGoogle Scholar
- Bertsekas DP (1981) A new algorithm for the assignment problem. Math Program 21(1):152–171MathSciNetzbMATHCrossRefGoogle Scholar
- Bloch F, Ryder H (2000) Two-sided search, marriage and matchmakers. Int Econ Rev 41(1):93–115CrossRefGoogle Scholar
- Bunkers SS (2012) The lived experience of feeling disappointed a parse research method study. Nurs Sci Q 25(1):53–61CrossRefGoogle Scholar
- Chakraborty D, Guha D, Dutta B (2016) Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization. Soft Comput 20(6):2245–2259CrossRefGoogle Scholar
- Chen X, Li Z, Fan Z-P, Zhou X, Zhang X (2016) Matching demanders and suppliers in knowledge service: a method based on fuzzy axiomatic design. Inf Sci 346–347:130–145MathSciNetCrossRefGoogle Scholar
- Clancy A, Vince R, Gabriel Y (2012) That unwanted feeling: a psychodynamic study of disappointment in organizations. Br J Manag 23(4):518–531CrossRefGoogle Scholar
- Cohon JL (1978) Multiobjective programming and planning. Academic Press, New YorkzbMATHGoogle Scholar
- Delquié P, Cillo A (2006) Disappointment without prior expectation: a unifying perspective on decision under risk. J Risk Uncertain 33:197–215zbMATHCrossRefGoogle Scholar
- Dur UM, Ünver MU (2015) Two-sided matching via balanced exchange: tuition and worker exchanges. Working Paper, 2015Google Scholar
- Echenique F (2008) What matchings can be stable? The testable implications of matching theory. Math Oper Res 33(3):757–768MathSciNetzbMATHCrossRefGoogle Scholar
- Ehlers L (2008) Truncation strategies in matching markets. Math Oper Res 33(2):327–335MathSciNetzbMATHCrossRefGoogle Scholar
- Fan ZP, Yue Q, Feng B, Liu Y (2010) An approach to group decision-making with uncertain preference ordinals. Comput Ind Eng 58(1):51–57CrossRefGoogle Scholar
- Gale D (2001) The two-sided matching problem: origin, development and current issues. Int Game Theory Rev 3(2–3):237–252MathSciNetzbMATHCrossRefGoogle Scholar
- Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15MathSciNetzbMATHCrossRefGoogle Scholar
- Grant S, Kajii A (1998) AUSI expected utility: an anticipated utility theory of relative disappointment aversion. J Econ Behav Organ 37(3):277–290CrossRefGoogle Scholar
- Gujar S, Faltings B (2015) Dynamic task assignments: an online two sided matching approach. In: 3rd International workshop on matching under preferences, MATCHUPGoogle Scholar
- Gul F (1991) A theory of disappointment aversion. Econometrica 59:667–686MathSciNetzbMATHCrossRefGoogle Scholar
- Hałaburda H (2010) Unravelling in two-sided matching markets and similarity of preferences. Games Econ Behav 69(2):365–393MathSciNetzbMATHCrossRefGoogle Scholar
- Halldórsson MM, Iwama K, Miyazaki S, Yanagisawa H (2004) Randomized approximation of the stable marriage problem. Theor Comput Sci 325(3):439–465zbMATHCrossRefGoogle Scholar
- Inman JJ, Dyer JS, Jia JM (1997) A generalized utility model of disappointment and regret effects on post-choice valuation. Market Sci 16(2):97–111CrossRefGoogle Scholar
- Irving RW, Manlove DF, Scott S (2008) The stable marriage problem with master preference lists. Discret Appl Math 156(15):2959–2977MathSciNetzbMATHCrossRefGoogle Scholar
- Iwama K, Manlove D, Miyazaki S, Morita Y (1999) Stable marriage with incomplete lists and ties. In: Proceedings of the ICALP’99: the 26th international colloquium on automata, languages, and programming, lecture notes in computer science, vol 1644. Springer, Berlin, pp 443–452zbMATHCrossRefGoogle Scholar
- Iwama K, Miyazaki S, Yamauchi NA (2008) \((2-c/\sqrt{N})\)-approximation algorithm for the stable marriage problem. Algorithmica 51(3):342–356MathSciNetzbMATHGoogle Scholar
- Jiang ZZ, Ip WH, Lau HCW, Fan Z-P (2011) Multi-objective optimization matching for one-shot multi-attribute exchanges with quantity discounts in e-brokerage. Expert Syst Appl 38(4):4169–4180CrossRefGoogle Scholar
- Jiang ZZ, Zhang R, Fan Z-P, Chen X (2015) A fuzzy matching model with hurwicz criteria for one-shot multi-attribute exchanges in e-brokerage. Fuzzy Optim Decis Mak 14(1):77–96MathSciNetCrossRefGoogle Scholar
- Klaus B, Klijn F (2006) Median stable matching for college admissions. Int J Game Theory 34(1):1–11MathSciNetzbMATHCrossRefGoogle Scholar
- Laciana CE, Weber EU (2008) Correcting expected utility for comparisons between alternative outcomes: a unified parameterization of regret and disappointment. J Risk Uncertain 36:1–17zbMATHCrossRefGoogle Scholar
- Liu X, Ma H (2015) A two-sided matching decision model based on uncertain preference sequences. Math Probl Eng 2015(1):1–10Google Scholar
- Loomes G, Sugden R (1986) Disappointment and dynamic consistency in choice under uncertainty. Rev Econ Stud 53(2):271–282MathSciNetzbMATHCrossRefGoogle Scholar
- Lu J, Wang X, Zhang L, Zhao X (2014) Fuzzy random multi-objective optimization based routing for wireless sensor networks. Soft Comput 18(5):981–994CrossRefGoogle Scholar
- Manlove DF, Irving RW, Iwama K, Miyazaki S, Morita Y (2002) Hard variants of stable marriage. Theor Comput Sci 276(1–2):261–279MathSciNetzbMATHCrossRefGoogle Scholar
- Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1):32–38MathSciNetzbMATHCrossRefGoogle Scholar
- Ohta N, Kuwabara K (2014) An integer programming approach for two-sided matching with indifferences. In: International conference on computational collective intelligence, 2014. Springer, pp 563–572Google Scholar
- Pais J (2008) Random matching in the college admissions problem. Econ Theory 35(1):99–116MathSciNetzbMATHCrossRefGoogle Scholar
- Qiu J, Feng G, Gao H (2013a) Static-output-feedback, control of continuous-time T–S fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans Fuzzy Syst 21(2):245–261CrossRefGoogle Scholar
- Qiu J, Tian H, Lu Q, Gao H (2013b) Nonsynchronized robust filtering design for continuous-time t–s fuzzy affine dynamic systems based on piecewise Lyapunov functions. IEEE Trans Cybern 43(6):1755–1766CrossRefGoogle Scholar
- Qiu J, Wei Y, Karimi HR (2014) New approach to delay-dependent H \(\infty \) H \(\infty \) mathcontainer loading mathjax, control for continuous-time markovian jump systems with time-varying delay and deficient transition descriptions. J Frankl Inst 352(1):189–215Google Scholar
- Qiu J, Gao H, Ding SX (2016a) Recent advances on fuzzy-model-based nonlinear networked control systems: a survey. IEEE Trans Ind Electron 63(2):1207–1217CrossRefGoogle Scholar
- Qiu J, Ding SX, Gao H, Yin S (2016b) Fuzzy-model-based reliable static output feedback, control of nonlinear hyperbolic PDE systems. IEEE Trans Fuzzy Syst 24(2):388–400CrossRefGoogle Scholar
- Roth AE (1985) Conflict and coincidence of interest in job matching: some new results and open questions. Math Oper Res 10:379–389MathSciNetzbMATHCrossRefGoogle Scholar
- Roth AE, Rothblum UG, Vande Vate JH (1993) Stable matching, optimal assignments and linear programming. Math Oper Res 18(4):803–828MathSciNetzbMATHCrossRefGoogle Scholar
- Rothblum UG (1992) Characterization of stable matchings as extreme points of a polytope. Math Program 54(1):57–67MathSciNetzbMATHCrossRefGoogle Scholar
- Sasaki H, Toda M (1996) Two-sided matching problems with externalities. J Econ Theory 70(1):93–110MathSciNetzbMATHCrossRefGoogle Scholar
- Sim KM, Chan RA (2000) A brokering protocol for agent-based e-commerce. IEEE Trans Syst Man Cybern C Appl Rev 30(4):474–484CrossRefGoogle Scholar
- Teo CP, Sethuraman J (1998) The geometry of fractional stable matchings and its applications. Math Oper Res 23(4):874–891MathSciNetzbMATHCrossRefGoogle Scholar
- Teo CP, Sethuraman J, Tan WP (2001) Gale-shapley stable marriage problem: revisited strategic issues and applications. Manag Sci 47(9):1252–1267zbMATHCrossRefGoogle Scholar
- Vande Vate JH (1989) Linear programming brings marital bliss. Oper Res Lett 8(3):147–153MathSciNetzbMATHCrossRefGoogle Scholar
- Von Neumann J, Morgensterm O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonGoogle Scholar
- Yue Q, Li Y (2014) Two-sided matching considering the preferences of agents and intermediary. Comput Model New Technol 18(11):832–835Google Scholar