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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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[2] Straffin Philip D. Jr., “$N$-Person Prisoners Dilemma”, Part III, Chapter 21, Game theory and strategy, Ser. Anneli Lax New Mathematical Library, 36, MAA Press, 1993, 139–144

[3] Grinikh A. L., “Stochastic $n$-person Prisoner's dilemma: the time-consistency of core and Shapley value”, Contributions to Game Theory and Management, 12 (2019), 151–158