Geodesic
An Effective Punishment for an n-Person Prisoner's Dilemma on a Network
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 256-262

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

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.
Keywords: prisoner's dilemma, network game, effective punishment. 
@article{TIMM_2021_27_3_a20,
     author = {A. L. Grinikh and L. A. Petrosyan},
     title = {An {Effective} {Punishment} for an {n-Person} {Prisoner's} {Dilemma} on a {Network}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {256--262},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a20/}
}
TY  - JOUR
AU  - A. L. Grinikh
AU  - L. A. Petrosyan
TI  - An Effective Punishment for an n-Person Prisoner's Dilemma on a Network
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2021
SP  - 256
EP  - 262
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a20/
LA  - en
ID  - TIMM_2021_27_3_a20
ER  - 
%0 Journal Article
%A A. L. Grinikh
%A L. A. Petrosyan
%T An Effective Punishment for an n-Person Prisoner's Dilemma on a Network
%J Trudy Instituta matematiki i mehaniki
%D 2021
%P 256-262
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a20/
%G en
%F TIMM_2021_27_3_a20
A. L. Grinikh; L. A. Petrosyan. An Effective Punishment for an n-Person Prisoner's Dilemma on a Network. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 256-262. http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a20/