Automation and Remote Control

, Volume 79, Issue 9, pp 1722–1731 | Cite as

Models of Two-Stage Mutual Best Choice

  • S. I. DotsenkoEmail author
  • A. A. Ivashko
Mathematical Game Theory and Applications


In this paper, we develop and study a game-theoretic model of mutual choice with two types of agents (groups) as follows. Each agent wants to make a couple with another agent from the opposite group. In contrast to classical best-choice models, two agents make a couple only by mutual agreement. We consider two setups, namely, natural mating (each agent acts in accordance with personal interests) and artificial selection (forced mating to maximize the average quality of couples). In the first case, the Nash equilibrium is determined; in the second case, an optimal selection procedure is designed. We analyze some modifications of the problem with different payoff functions and incomplete information.


mutual choice population natural mating selection Nash equilibrium 


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  1. 1.
    Gusein-Zade, S.M., The Problem of Choice and the Optimal Stopping Rule for a Sequence of Independent Trials, Theory Probab. Appl., 1966, vol. 11(3), pp. 472–476.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dotsenko, S.I., The Problem of Choice of the Best Object as a Two-Person Game, Kibern. Vych. Tekhnika, 2011, no. 164, pp. 43–53.Google Scholar
  3. 3.
    Dynkin, E.B. and Yushkevich, A.A., Teoremy i zadachi o protsessakh Markova (Theorems and Problems for Markov Processes), Moscow: Nauka, 1967, pp. 91–102.Google Scholar
  4. 4.
    Mazalov, V.V., Mathematical Game Theory and Applications, New York: Wiley, 2014.zbMATHGoogle Scholar
  5. 5.
    Alpern, S. and Reyniers, D., Strategic Mating with Common Preferences, J. Theor. Biol., 2005, vol. 237, pp. 337–354.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Alpern, S., Katrantzi, I., and Ramsey, D., Equilibrium Population Dynamics When Mating Is by Mutual Choice Based on Age, Theor. Populat. Biol., 2014, vol. 94, pp. 63–72.CrossRefGoogle Scholar
  7. 7.
    Chow, Y., Moriguti, D., Robbins, H., and Samuels, S., Optimal Selection Based on Relative Rank (the “Secretary Problem”), Israel J. Math., 1964, vol. 2, pp. 81–90.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Eriksson, K., Strimling, P., and Sjostrand, J., Optimal Expected Rank in a Two-Sided Secretary Problem, Oper. Res., 2007, vol. 55, no. 5, pp. 921–931.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Gale, D. and Shapley, L.S., College Admissions and the Stability of Marriage, Am. Math. Monthly, 1962, vol. 69(1), pp. 9–15.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gilbert, J. and Mosteller, F., Recognizing the Maximum of a Sequence, J. Am. Stat. Assoc., 1966, vol. 61, pp. 35–73.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ivashko, A.A. and Konovalchikova, E.N., Equilibrium Strategies in Two-Sided Mate Choice Problem with Age Preferences, Contrib. Game Theory Manage., 2014, vol. 7, pp. 142–150MathSciNetzbMATHGoogle Scholar
  12. 12.
    Mazalov, V. and Falko, A., Nash Equilibrium in Two-Sided Mate Choice Problem, Int. Game Theory Rev., 2008, vol. 10(4), pp. 421–435.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    McNamara, J. and Collins, E., The Job Search Problem as an Employer-Candidate Game, J. Appl. Prob., 1990, vol. 28, pp. 815–827.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Moser, L., On a Problem of Cayley, Scripta Math., 1956, vol. 22, no. 5, pp. 289–292.zbMATHGoogle Scholar
  15. 15.
    Roth, A. and Sotomayor, M., Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge: Cambridge Univ. Press, 1992.zbMATHGoogle Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.Institute of Applied Mathematical Research, Karelian Research CenterRussian Academy of SciencesPetrozavodskRussia

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