TY - JOUR

T1 - Subgame consistent cooperative behavior in an extensive form game with chance moves

AU - Kuzyutin, Denis

AU - Smirnova, Nadezhda

N1 - Publisher Copyright: © 2020 by the authors.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We design a mechanism of the players' sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players' rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players' attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player's optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism.

AB - We design a mechanism of the players' sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players' rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players' attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player's optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism.

KW - Chance moves

KW - Cooperative trajectory

KW - Imputation distribution procedure

KW - Multistage game

KW - Subgame perfect equilibria

KW - Time consistency

KW - CORE

KW - cooperative trajectory

KW - chance moves

KW - time consistency

KW - multistage game

KW - subgame perfect equilibria

KW - SHAPLEY VALUE

KW - imputation distribution procedure

UR - http://www.scopus.com/inward/record.url?scp=85088441345&partnerID=8YFLogxK

U2 - 10.3390/MATH8071061

DO - 10.3390/MATH8071061

M3 - Article

AN - SCOPUS:85088441345

VL - 8

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 7

M1 - 1061

ER -