Research output: Contribution to journal › Article › peer-review
Subgame consistent cooperative behavior in an extensive form game with chance moves. / Kuzyutin, Denis; Smirnova, Nadezhda.
In: Mathematics, Vol. 8, No. 7, 1061, 01.07.2020.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 61417383