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Of all publications in the section: 10
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Article
Karpov A. V. Mathematical Social Sciences. 2015. Vol. 74. P. 1-7.
This paper studies the incentives for alliance (coalition) formation. It provides an example of an alliance that leads to unlimited seat gains. A full description of a set that guarantees the lack of successful alliance is found. The probability of the lack of successful alliances is evaluated. A game-theoretical approach for alliance formation is applied.
Article
Alexander A. Lazarev, Gafarov E. R., Wernerb F. Mathematical Social Sciences. 2013. Vol. 65. No. 3. P. 232.

In the article E.R. Gafarov, A.A. Lazarev, F. Werner, Single machine scheduling problems with financial resource constraints: Some complexity results and properties, Mathematical Social Sciences, 62 (2011), 7–13, the following mistake is found in Section 3.2, where the authors consider the problem denoted as 1|NR, dj = d, gj = g|  Tj and claim that it is NP-hard. In the proof, a reduction from the Partition Problem was used which is not polynomial, since M exponentially depends on n. However, it is not difficult to correct this proof. The main idea of using Mn−i+1 was that the processing time of a job belongs to a pair with the smallest number being greater than the total sum of the processing times of all jobs from the pairs with larger numbers, e.g., for the job V2: p2 ≫ n i=2(p2i−1 + p2i). Instead of using p2i = Mn−i+1, where M = (n  bj)n (see the definition of the instance given in (3) on page 11), we can consider, e.g., p2i = 2n • 2n−i+1M, where M = (n  bj). In this case, the reduction will be polynomial in the input length, if we suppose that all digits used are coded in a binary system with approximately 2n zero–one symbols per digit.

Article
Aleskerov F. T., Yakuba V. I., Юзбашев Д. В. Mathematical Social Sciences. 2007. Vol. 53. P. 106-110.
Article
Dietzenbacher B. Mathematical Social Sciences. 2018. Vol. 92. P. 16-21.

This paper analyzes bankruptcy games with nontransferable utility as a generalization of bankruptcy games with monetary payoffs. Following the game theoretic approach to NTU-bankruptcy problems, we study some appropriate properties and the core of NTU-bankruptcy games. Generalizing the core cover and the reasonable set to the class of NTU-games, we show that NTU-bankruptcy games are compromise stable and reasonable stable. Moreover, we derive a necessary and sufficient condition for an NTU-bankruptcy rule to be game theoretic.

Article
Rubchinskiy A. Mathematical Social Sciences. 2010. Vol. 60. No. 1. P. 1-14.

In this article, the fairdivision problem for two participants in the presence of both divisible and indivisibleitems is considered. Three interrelated modifications of the notion of fairdivision–profitably, uniformly and equitably fairdivisions–were introduced. Computationally efficient algorithm for finding all of them was designed. The algorithm includes repetitive solutions of integer knapsack-type problems as its essential steps. The necessary and sufficient conditions of the existence of proportional and equitable division were found. The statements of the article are illustrated by various examples.

Article
Moulin H. Mathematical Social Sciences. 2016.

In the bilateral assignment problem, source a holds the amount ra of resource of type a, while sink i must receive the total amount xi of the various resources. We look for assignment rules meeting the powerful separability property known as Consistency: “every subassignment of a fair assignment is fair”. They are essentially those rules selecting the feasible flow minimizing the sum ∑i,aW(yia), where W is smooth and strictly convex.

Article
Zakharenko R. Mathematical Social Sciences. 2016. No. 80. P. 58-64.

This paper seeks answers to two questions. First, if a greater social activity of an individual enhances oblique (i.e. to non-relatives) transmission of her cultural traits at the expense of vertical (i.e. to children) transmission as well as family size, which behavior is optimal from cultural evolution standpoint? I formalize a general model that characterizes evolutionarily stable social activity. The proposed model replicates the theory of Newson et al. (2007) that fertility decline is caused by increasing role of oblique cultural transmission. Second, if social activity is a rational choice rather than a culturally inherited trait, and if cultural transmission acts on preferences rather than behaviors, which preferences survive the process of cultural evolution? I arrive at a very simple yet powerful result: under mild assumptions on model structure, only preferences which emphasize exclusively the concern for social prestige, i.e. extent to which one’s cultural trait has been picked up by others, survive.

Article
Aleskerov F. T., Karabekyan D., Yakuba V. I. et al. Mathematical Social Sciences. 2012. Vol. 64. No. 1. P. 67-73.

By extending manipulability indices defined for single-valued social choice rules to the multi-valued case, we explore the degree of manipulability of seven multi-valued social choice rules. Our analysis is based on computational experiments.

Article
Gafarov E., Lazarev A. A., Werner F. Mathematical Social Sciences. 2011. No. 62. P. 7-13.

We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity results. Particular attention is given to the problem of minimizing total tardiness. In addition, for the so-called budget scheduling problem with minimizing the makespan, we present some properties of feasible schedules.