On the model of the best bilateral two-stage mutual choice
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 1, pp. 45-61.

Voir la notice de l'article provenant de la source Math-Net.Ru

A mutual choice model with two types of agents, who want to make a couple with opposite side agents is investigated. Unlike classical best-choice models two agents make a couple only by mutual agreement. Two statements are considered: natural mating and artificial selection. In the first case the Nash equilibrium is determined, in the second case the optimal selection routine is found. Several versions of the problem and incomplete information scenario are considered.
Keywords: mutual choice, natural mating, selection, Nash equilibrium.
Mots-clés : population
@article{MGTA_2017_9_1_a2,
     author = {Sergei I. Dotsenko and Anna A. Ivashko},
     title = {On the model of the best bilateral two-stage mutual choice},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {45--61},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2017_9_1_a2/}
}
TY  - JOUR
AU  - Sergei I. Dotsenko
AU  - Anna A. Ivashko
TI  - On the model of the best bilateral two-stage mutual choice
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2017
SP  - 45
EP  - 61
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2017_9_1_a2/
LA  - ru
ID  - MGTA_2017_9_1_a2
ER  - 
%0 Journal Article
%A Sergei I. Dotsenko
%A Anna A. Ivashko
%T On the model of the best bilateral two-stage mutual choice
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2017
%P 45-61
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2017_9_1_a2/
%G ru
%F MGTA_2017_9_1_a2
Sergei I. Dotsenko; Anna A. Ivashko. On the model of the best bilateral two-stage mutual choice. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 1, pp. 45-61. http://geodesic.mathdoc.fr/item/MGTA_2017_9_1_a2/

[1] Gusein-Zade S. M., “Zadacha vybora i optimalnoe pravilo ostanovki posledovatelnosti nezavisimykh ispytanii”, TVP, 11:3 (1966), 534–537 | Zbl

[2] Dotsenko S. I., “Zadacha vybora nailuchshego ob'ekta kak igra dvukh lits”, Kibernetika i Vychislitelnaya tekhnika, 2011, no. 164, 43–53

[3] Dynkin E. B., Yushkevich A. A., Teoremy i zadachi o protsessakh Markova, Nauka, M., 1967, 91–102

[4] Mazalov V. V., Matematicheskaya teoriya igr i prilozheniya, Izd-vo «Lan», SPb., 2010

[5] Alpern S., Reyniers D., “Strategic mating with common preferences”, Journal of Theoretical Biology, 237 (2005), 337–354 | DOI | MR

[6] Alpern S., Katrantzi I., Ramsey D., “Equilibrium population dynamics when mating is by mutual choice based on age”, Theoretical Population Biology, 94 (2014), 63–72 | DOI

[7] Chow Y., Moriguti D., Robbins H., Samuels S., “Optimal selection based on relative rank (the "Secretary problem")”, Israel J. Math., 2 (1964), 81–90 | DOI | MR | Zbl

[8] Eriksson K., Strimling P., Sjostrand J., “Optimal expected rank in a two-sided secretary problem”, Oper. Res., 55:5 (2007), 921–931 | DOI | MR | Zbl

[9] Gale D., Shapley L. S., “College Admissions and the Stability of Marriage”, The American Mathematical Monthly, 69:1 (1962), 9–15 | DOI | MR | Zbl

[10] Gilbert J., Mosteller F., “Recognizing the maximum of a sequence”, J. of Amer. Stat. Assoc., 61 (1966), 35–73 | DOI | MR

[11] Ivashko A. A., Konovalchikova E. N., “Equilibrium strategies in two-sided mate choice problem with age preferences”, Contributions to Game Theory and Management, 7 (2014), 142–150 | MR

[12] Mazalov V., Falko A., “Nash equilibrium in two-sided mate choice problem”, International Game Theory Review, 10:4 (2008), 421–435 | DOI | MR | Zbl

[13] McNamara J., Collins E., “The job search problem as an employer-candidate game”, J. Appl. Prob., 28 (1990), 815–827 | MR

[14] Moser L., “On a problem of Cayley”, Scripta Math., 22:5 (1956), 289–292

[15] Roth A., Sotomayor M., Two-sided matching: A study in game-theoretic modeling and analysis, Cambridge University Press, 1992 | MR | Zbl