Abstract:
The paper considers an n-person prisoner's dilemma game. We present a modification of this model for the network interaction of players. A set of grim trigger strategies is a Nash equilibrium in the repeated n-person prisoner's dilemma on a network, just as in the two-player game. However, even a slight deviation leads to the case where players get low payoffs in perpetuity without the possibility of returning to the Pareto optimal payoffs. A solution to this problem is proposed. The players' payoff functions in a game of an n-person prisoner's dilemma type on a network are described. A strategy involving a punishment on a limited interval of the game is proposed. The number of steps required for an effective punishment is found. An example of a network for this game is given. The number of steps for an effective punishment is found for the given example.
Citation:
A. L. Grinikh, L. A. Petrosyan, “An Effective Punishment for an n-Person Prisoner's Dilemma on a Network”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 256–262
\Bibitem{GriPet21}
\by A.~L.~Grinikh, L.~A.~Petrosyan
\paper An Effective Punishment for an n-Person Prisoner's Dilemma on a Network
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 256--262
\mathnet{http://mi.mathnet.ru/timm1854}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-3-256-262}
\elib{https://elibrary.ru/item.asp?id=46502706}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123582639}
Linking options:
https://www.mathnet.ru/eng/timm1854
https://www.mathnet.ru/eng/timm/v27/i3/p256
This publication is cited in the following 7 articles:
R. Yu. Kazimirova, G. I. Ibragimov, R. M. Hasim, “Multi-pursuer pursuit differential game for an infinite system of second order differential equations”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:1 (2024), 48–64
Alena M. Pisareva, Elena M. Parilina, “Priblizhennoe ravnovesie v konechno povtoryayuscheisya igre «Dilemma zaklyuchennogo»”, MTIP, 16:2 (2024), 45–65
Vladimir N. Ushakov, Aleksandr M. Tarasev, Andrei V. Ushakov, “Minimaksnaya differentsialnaya igra s fiksirovannym momentom okonchaniya”, MTIP, 16:3 (2024), 77–112
V. N. Ushakov, A. V. Ushakov, O. A. Kuvshinov, “Sblizhenie konfliktno upravlyaemykh sistem na konechnom promezhutke vremeni”, Izv. IMI UdGU, 64 (2024), 70–96
V. N. Ushakov, A. M. Tarasyev, A. A. Ershov, “Concerning one supplement to unification method of N.N. Krasovskii in differential games theory”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 65–71
Aleksandra L. Grinikh, “Cooperation in the multi-agent system with different types of interactions”, Contributions to Game Theory and Management, 15 (2022), 60–80
Aleksandra L. Grinikh, Leon A. Petrosyan, “Cooperative n-person prisoner's dilemma on a network”, Contributions to Game Theory and Management, 14 (2021), 122–126
Citation in format AMSBIB
Contact us: