Geodesic
Cooperation in the multi-agent system with different types of interactions
Contributions to game theory and management, Tome 15 (2022), pp. 60-80.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 time-consistent subset of the core of the dynamic game. In accordance with this type of game we consider some specific properties of players' payoffs and construct the new way of their interactions. Using the network representation, the classic model is modified to the wider class of games that allows to specify players' influence to each other's payoff function. These investigations can be used for the description of cooperation in the other multi-agent systems.
Keywords: $n$-person prisoner's dilemma, cooperative game, characteristic function, network game, Shapley value. 
@article{CGTM_2022_15_a6,
     author = {Aleksandra L. Grinikh},
     title = {Cooperation in the multi-agent system with different types of interactions},
     journal = {Contributions to game theory and management},
     pages = {60--80},
     publisher = {mathdoc},
     volume = {15},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2022_15_a6/}
}
TY  - JOUR
AU  - Aleksandra L. Grinikh
TI  - Cooperation in the multi-agent system with different types of interactions
JO  - Contributions to game theory and management
PY  - 2022
SP  - 60
EP  - 80
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2022_15_a6/
LA  - en
ID  - CGTM_2022_15_a6
ER  - 
%0 Journal Article
%A Aleksandra L. Grinikh
%T Cooperation in the multi-agent system with different types of interactions
%J Contributions to game theory and management
%D 2022
%P 60-80
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2022_15_a6/
%G en
%F CGTM_2022_15_a6
Aleksandra L. Grinikh. Cooperation in the multi-agent system with different types of interactions. Contributions to game theory and management, Tome 15 (2022), pp. 60-80. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a6/

[1] Aumann, R. J., “Acceptable points in general cooperative n-person games”, Contributions to the Theory of Games, v. 4, AM, 40, 1959, 287–324 | MR | Zbl

[2] Carroll, J. W., “Iterated N-player prisoner's dilemma games”, Philosophical Studies, 53:3 (1988), 411–415 | DOI | MR

[3] Grinikh, A. L., “Stochastic n-person prisoner's dilemma: the time-consistency of core and Shapley value”, Contributions to Game Theory and Management, XII (2019), 151–158 | MR

[4] Grinikh, A. L. and Petrosyan, L. A., “An Effective Punishment for an n-Person Prisoner's Dilemma on a Network”, Trudy Instituta matematiki i mekhaniki UrO RAN, 27, no. 3, 2021, 256–262 | DOI | MR

[5] Grinikh, A. L. and Petrosyan, L. A., “Shapley value of n-person prisoner's dilemma”, Journal of Physics: Conference Series, 1864:1 (2021), 012061 | DOI | MR

[6] Grinikh, A. L. and Petrosyan, L. A., “Cooperative n-person Prisoner's Dilemma on a Network”, Contributions to Game Theory and Management, 14 (2021), 122–126 | DOI | MR

[7] Hamburger, H., “N-person prisoner's dilemma”, Journal of Mathematical Sociology, 3:1 (1973), 27–48 | DOI | MR | Zbl

[8] Petrosyan, L. A., Differential games of pursuit, v. 2, World Scientific, 1993, 312 pp. | MR | Zbl

[9] Petrosyan, L., “Strong Strategic Support of Cooperation in Multistage Games”, International Game Theory Review (IGTR), 21:1 (2019), 1–12 | MR | Zbl

[10] Petrosjan, L. A. and Grauer, L. V., “Strong Nash equilibrium in multistage games”, International Game Theory Review, 4:2 (2002), 255–264 | DOI | MR | Zbl

[11] Petrosyan, L. A. and Grauer, L. V., “Multistage games”, Journal of applied mathematics and mechanics, 68:4 (2004), 597–605 | DOI | MR | Zbl

[12] Petrosyan, L. A. and Pankratova, Y. B., “New characteristic function for multistage dynamic games”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 14:4 (2018), 316–324 | MR

[13] Shapley, L. S., “A value for n-person games”, Contributions to the Theory of Games, 2:28 (1953), 307–317 | MR

[14] Straffin, P. D., Game theory and strategy, MAA, 36, 1993 | MR | Zbl