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Cooperative n-person prisoner's dilemma on a network
P. 122–126.
Grinikh A., Petrosyan L.
In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the influence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.
In book
Vol. XIV: Collected papers. , St. Petersburg: St. Petersburg University, 2021.
Aleksandra L. Grinikh, , in: Contributions to Game Theory and Management, Vol. XVVol. 15.: St. Petersburg: Saint Petersburg State University, 2022. Ch. 7 P. 60–80.
This paper summarizes the list of our works that contain researches about optimality principles for the "n-person prisoner’s dilemma" game. The classic model is considered through the new payoff function for each player that allows to consider it without restrictions for the number of players. The new characteristic function gives an opportunity to introduce the ...
Added: October 31, 2024
V. V. Gusev, Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2024 Vol. 18 No. 2 P. 271–281
The paper examines the problem of the distribution of public space. We use the methods of cooperative game theory to solve this problem. Players are districts, while the value of the characteristic function is the total number of people interested in a particular type of public space in the areas under consideration. The axioms that ...
Added: September 10, 2024
A. S. Shvedov, Mathematical notes 2023 Vol. 114 No. 4 P. 619–624
It is proved that the bargaining set for a cooperative game with trapezoidal fuzzy payoffs is nonempty ...
Added: October 18, 2023
Shvedov A. S., Математические заметки 2023 Т. 114 № 4 С. 615–622
It is proved that the bargaining set for a cooperative game with trapezoidal fuzzy payoffs is nonempty. ...
Added: October 6, 2023
Shvedov A. S., Информатика и ее применения 2022 Т. 16 № 3 С. 2–6
Zhao (2001) suggested a new condition for non-emptiness of the core of a cooperative game. At first, a necessary and sufficient condition was found by Zhao for a particular case of games with transferable utility. In this case, as was shown by Zhao, the condition can be easily used for construction of a computational scheme, ...
Added: October 12, 2022
Antonov D., Burovskiy E., Shchur L., Physical Review Research 2021 Vol. 3 Article L032072
We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of
Nowak and May, based on the Prisoner’s dilemma, and augment the game rules by a self-consistent mean-field
term. This way, an agent operates based on local information from its neighbors and nonlocal information via
the mean-field coupling. We simulate the model ...
Added: September 24, 2021
Shvedov A. S., Mathematical notes 2021 Vol. 110 No. 2 P. 261–266
It is well known that, for cooperative games with transferable utility (and with crisp
payoffs), the set of reasonable imputations is nonempty. It is also known for what values of ε the
set of reasonable imputations belongs to the ε-core. Then the ε-core is also nonempty. This result
is of considerable interest, because the 0-core of a cooperative ...
Added: August 5, 2021
Shvedov A. S., Математические заметки 2021 Т. 110 № 2 С. 282–288
It is well known that, for cooperative games with transferable utility (and with crisp
payoffs), the set of reasonable imputations is nonempty. It is also known for what values of ε the
set of reasonable imputations belongs to the ε-core. Then the ε-core is also nonempty. This result
is of considerable interest, because the 0-core of a cooperative ...
Added: August 5, 2021
E.B.Yanovskaya, Automation and Remote Control 2018 Vol. 79 No. 12 P. 2237–2258
A weakening of the property covariance named self-covariance is defined. Sels-covariant solutions are positively homogenous and satisfy a "restricted" translation covariance so that feasible shifts are only the solution vectors and their multipliers. A description of all non-empty, single-valued,efficient,anonytmous, weakly and self-covariant solutions inn the class of two-person games is given. As demonstrated below, among ...
Added: October 29, 2019
Burovskiy E., Малютин А. А., Shchur L., / Series cond-mat "arxiv.org". 2018. No. arXiv:1811.08784.
We study a model of a spatial evolutionary game, based on the Prisoner's dilemma for two regular arrangements of players, on a square lattice and on a triangular lattice. We analyze steady state distributions of players which evolve from irregular, random initial configurations. We find significant differences between the square and triangular lattice, and we ...
Added: November 21, 2018
Avrachenkov K. E., Kondratev Aleksei Y, Mazalov V. V. et al., Computational Social Networks 2018 Vol. 5 No. 11 P. 1–28
The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we ...
Added: October 30, 2018
Колотев С. В., Малютин А. А., Burovskiy E. et al., Physica A: Statistical Mechanics and its Applications 2018 Vol. 499 P. 142–147
We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being ...
Added: February 4, 2018
Skorobogatov A., Историко-экономические исследования 2017 Т. 18 № 3 С. 511–544
The article examines the relationship between power resource and rational behavior in history. It is shown that personal interest is expressed in socially useful economic activities of individuals only if they had no adequate power potential. This general principle is illustrated by examples of Russian medieval history that are associated with the specifics of the ...
Added: January 29, 2018
Колотев С. В., Малютин А. А., Burovskiy E. et al., Journal of Physics: Conference Series 2018 Vol. 955 No. 012023 P. 1–6
We investigate geometrical aspects of a spatial evolutionary game. The game is based on the Prisoner's dilemma. We analyze the geometrical structure of the space distribution of cooperators and defectors in the steady-state regime of evolution. We develop algorithm for the identification of the interfaces between clusters of cooperators and defectors, and measure fractal properties ...
Added: November 14, 2017
Petrosian O., Nastych M., Volf D., , in: 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings.: Institute of Electrical and Electronics Engineers Inc., 2017. Ch. 78 P. 1–4.
Non-transferable utility game of oil market is considered. Special approach for defining solution is used. This approach enables to construct a real time models of conflicting processes. Connection between the solution in the game with moving information horizon and solutions on the truncated time intervals is shown. ...
Added: September 14, 2017
Yanovskaya E. B., / NRU Higher School of Economics. Series EC "Economics". 2016. No. 127.
Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents [Moulin 2000] is extended to ...
Added: October 14, 2016
Elena Yanovskaya, Automation and Remote Control 2016 Vol. 77 No. 9 P. 1699– 1710
On the class of cooperative games with restricted cooperation the most popular solution -- the core -- may
be unbounded. The bounded core is the union of all bounded faces of the core. It can be empty even if
the core itself is not empty. Two axiomatizations of the bouded core atre ngiven: the first one
is ...
Added: October 13, 2016
Nastych M., Финансы и кредит 2015 Т. 43 № 667 С. 53–66
Importance The paper is devoted to analysis of the effectiveness of economic integration of firms. By efficiency I mean the standard requirements for profitability of integration (non-decreasing of total profit) in microeconomics, theory of the firm and the theory of industrial organization, or non-negativity of synergy in the theory of corporate finance and business valuation ...
Added: September 1, 2015
Yanovskaya E. B., , in: Contributions to game theory and managementIssue 3.: St. Petersburg: Graduate School of Management, St. Petersburg University, 2010. P. 421–430.
Interval cooperative games are models of cooperative situation where only bounds for payoffs of coalitions are known with certainty. The extension of solutions of classical cooperative games to interval setting highly depends on their monotonicity properties. However. both the prenucleolus and the tau-value are not aggregate monotonic on the class of convex TU games Hokari ...
Added: March 20, 2014