Grafy a teoria stabilnych alokacji

• Authors: Kozioł-Kaczorek Dorota , Pietrych Łukasz

Title variants

EN

Graphs and theory of stable allocation

• Languages of publication: PL

Abstracts

EN

The paper discusses a model of matching process which was proposed by two American mathematicians: David Gale and Lloyd S. Shapley. The basic concept defined by them was the stable allocation, which can be achieved with so-called deferred acceptance algorithm. The article analyzes the problems discussed by the theory of stable allocations on the basis of graph theory. It has been shown that the issues raised by this theory can be ana-lyzed using bipartite graphs and networks weighted. They also formulated conditions which should be met in purpose to solve a problem of matching. References relate to the labor market, as a discussed issue is applicable in practice, especially in the design of systems of recruitment companies. The aim of the article is to present the problem of bilateral associa-tions with the use of the language of graph theory and an indication of possible applications in the area of search and match of job seekers and employers.

Keywords

EN

associations; optimal allocation; graphs

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Econometrics. Ekonometria. Advances in Applied Data Analytics
• Year: 2016
• Issue: 3 (53)
• Pages: 102-114

Contributors

author

Kozioł-Kaczorek Dorota

author

Pietrych Łukasz

References

• Baïou M., 2016, A note on many-to-many matchings and stable allocations, Discrete Applied Math-ematics, 222, s. 181-184.
• Baïou M., Balinski M., 2007, Characterizations of the optimal stable allocation mechanism, Opera-tion Research Letters, 35, s. 392-402.
• Biró P., Fleiner T., 2010, Integral stable allocation problem on graphs, Discrete Optimization, 7, s. 64-73.
• Bronsztejn I.N., Siemiendiajew K.A., Musiol G., Mühlig, 2013, Nowoczesne kompendium matematy-ki, Wydawnictwo Naukowe PWN, Warszawa.
• Halmos P.R., Vaughan H.E., 1950, The marriage problem, American Journal of Mathematics, vol. 72, no. 1, s. 214-215.
• Lovász L., Plummer M.D., 1986, Matching Theory, North-Holland, Amsterdam.
• Roth A.E., 1984, The evolution of the labor market for medical interns and residents: A case study in game theory, Journal of Political Economy, no. 92, s. 991-1016.
• Roth A.E., 2002, The economist as engineer: Game theory, experimentation, and computation as tools for design economics, Econometrica, vol. 70, no. 4, s. 1341-1378.
• Roth A.E., Sotomayor M.A., 1992 Two-sided matching. A study in game theoretic modeling and analysis, http://web.stanford.edu/~alroth/papers/92_HGT_Two-SidedMatching.pdf (10.12.2015).
• Ruohonen K., 2013, Graph theory, Tampere University of Technology, http://math.tut.fi/~ruohonen/ GT_English.pdf (15.01.2016).
• Shapley L.S., Gale D., 1962, College admissions and the stability of marriage, The American Math-ematical Monthly, vol. 69, s. 9-15.
• Stankiewicz W., 2013, Kolejny sukces teorii gier: nobliści z ekonomii 2012, Ekonomia i Prawo, tom XII, nr 1/2013, s. 33-45.
• Świtalski Z., 2008, O kojarzeniu małżeństw i rekrutacji kandydatów do szkół, Rocznik Polskiego Towarzystwa Matematycznego, Seria II: Wiadomości Matematyczne, XLIV, s. 35-46.
• Wilson R.J. 2012, Wprowadzenie do teorii grafów, Wydawnictwo Naukowe PWN, Warszawa.
• Wojciechowski J., Pieńkosz K., 2013, Grafy i sieci, Wydawnictwo Naukowe PWN, Warszawa.