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  • 1. Andersson, O.
    et al.
    Argenton, C.
    Weibull, Jörgen W.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Stockholm School of Economics, Sweden.
    Robustness to strategic uncertainty in the Nash demand game2018In: Mathematical Social Sciences, ISSN 0165-4896, E-ISSN 1879-3118, Vol. 91, p. 1-5Article in journal (Refereed)
    Abstract [en]

    This paper studies the role of strategic uncertainty in the Nash demand game. A player's uncertainty about another player's strategy is modeled as an atomless probability distribution over that player's strategy set. A strategy profile is robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others (Andersson et al., 2014). In the context of the Nash demand game, we show that robustness to symmetric (asymmetric) strategic uncertainty singles out the (generalized) Nash bargaining solution. The least uncertain party obtains the bigger share.

  • 2. Eriksson, K.
    et al.
    Karlander, Johan
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Oller, L. E.
    Becker's assortative assignments: stability and fairness2000In: Mathematical Social Sciences, ISSN 0165-4896, E-ISSN 1879-3118, Vol. 39, no 2, p. 109-118Article in journal (Refereed)
    Abstract [en]

    Inspired by Roth and Sotomayor we make a deeper mathematical study of the assortative matching markets defined by Becker, finding explicit results on stability and fairness. We note that in the limit, when the size of the market tends to infinity. we obtain the continuous model of Sattinger and retrieve his characterization of the core of the game in this limit case. We also find that the most egalitarian core solution for employees is the employer-optimal assignment.

  • 3. Eriksson, Kirnmo
    et al.
    Sjöstrand, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Strimling, Pontus
    Three-dimensional stable matching with cyclic preferences2006In: Mathematical Social Sciences, ISSN 0165-4896, E-ISSN 1879-3118, Vol. 52, no 1, p. 77-87Article in journal (Refereed)
    Abstract [en]

    We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. Nonexistence of stable threesome matchings. Mathematical Social Sciences 16, 207-209] showed that not all instances of 3GSM allow stable matchings. Boros et al. [Boros, E., Gurvich, V, Jaslar, S., Krasner, D., 2004. Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematics 286, 1-10] showed that if preferences are cyclic, and the number of agents is limited to three of each gender, then a stable matching always exists. Here we extend this result to four agents of each gender. We also show that a number of well-known sufficient conditions for stability do not apply to cyclic 3GSM. Based on computer search, we formulate a conjecture on stability of "strongest link" 3GSM, which would imply stability of cyclic 3GSM.

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