TY - JOUR

T1 - Strong Subgame Consistency of the Core in Stochastic Network Formation Games

AU - Sun, Ping

AU - Parilina, Elena

N1 - Publisher Copyright: © 2022, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2024/3/1

Y1 - 2024/3/1

N2 - We consider a model of network formation as a stochastic game with random duration proposed initially in Sun and Parilina (Autom Remote Control 82(6):1065–1082, 2021). In the model, the leader first suggests a joint project to other players, i.e., the network connecting them. Second, the players are allowed to form fresh links with each other updating the initially proposed network. The stage payoff of any player is defined depending on the network structure. There are two types of randomness in the network formation process: (i) links may fail to be formed with different probabilities although players intend to establish them, (ii) the game process may terminate at any stage or transit to the next stage with a certain probability distribution. Finally, a network is formed as a result of players’ decisions and realization of random variables. The cooperative version of the stochastic game is investigated. In particular, we examine the properties of subgame consistency as well as strong subgame consistency of the core. We provide a payment mechanism or regularization of the core elements to sustain its subgame consistency and avoid the player’s deviations from the cooperative trajectory. In addition, the distribution procedure of the core elements is regularized in case there are negative payments to achieve only nonnegative payments to the players at any stage. The sufficient condition of a strongly subgame consistent core is also obtained. We illustrate our theoretical results with a numerical example.

AB - We consider a model of network formation as a stochastic game with random duration proposed initially in Sun and Parilina (Autom Remote Control 82(6):1065–1082, 2021). In the model, the leader first suggests a joint project to other players, i.e., the network connecting them. Second, the players are allowed to form fresh links with each other updating the initially proposed network. The stage payoff of any player is defined depending on the network structure. There are two types of randomness in the network formation process: (i) links may fail to be formed with different probabilities although players intend to establish them, (ii) the game process may terminate at any stage or transit to the next stage with a certain probability distribution. Finally, a network is formed as a result of players’ decisions and realization of random variables. The cooperative version of the stochastic game is investigated. In particular, we examine the properties of subgame consistency as well as strong subgame consistency of the core. We provide a payment mechanism or regularization of the core elements to sustain its subgame consistency and avoid the player’s deviations from the cooperative trajectory. In addition, the distribution procedure of the core elements is regularized in case there are negative payments to achieve only nonnegative payments to the players at any stage. The sufficient condition of a strongly subgame consistent core is also obtained. We illustrate our theoretical results with a numerical example.

KW - Core

KW - Network formation

KW - Stochastic game

KW - Strong subgame consistency

KW - 91A12

KW - 91A25

KW - 91A15

UR - http://www.scopus.com/inward/record.url?scp=85140953586&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6dd4c69b-5b9c-3ef9-9bec-2987b6124bc0/

U2 - 10.1007/s40305-022-00442-4

DO - 10.1007/s40305-022-00442-4

M3 - Article

AN - SCOPUS:85140953586

VL - 12

SP - 189

EP - 213

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

SN - 2194-668X

IS - 1

ER -