TY - JOUR

T1 - Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs

AU - Parilina, Elena M.

AU - Zaccour, Georges

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/7

Y1 - 2022/7

N2 - We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the tree structure is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the players’ beliefs and assume that the players agree to adopt one of them if they decide to cooperate. Second, we determine the Nash bargaining outcomes for the whole duration of the game. Finally, to insure sustainability of cooperation throughout the whole duration of the game, we propose two time-consistent decompositions over nodes of each player’s cooperative share, namely a proportion-consistent and a node-consistent allocation schemes. We illustrate our results with a simple Cournot oligopoly with capacity constraints.

AB - We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the tree structure is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the players’ beliefs and assume that the players agree to adopt one of them if they decide to cooperate. Second, we determine the Nash bargaining outcomes for the whole duration of the game. Finally, to insure sustainability of cooperation throughout the whole duration of the game, we propose two time-consistent decompositions over nodes of each player’s cooperative share, namely a proportion-consistent and a node-consistent allocation schemes. We illustrate our results with a simple Cournot oligopoly with capacity constraints.

KW - Asymmetric information

KW - Belief aggregation

KW - Event tree

KW - Nash bargaining solution

KW - S-adapted strategies

KW - Stochastic games

KW - CONSISTENT SHAPLEY VALUE

KW - STABILITY

KW - EQUILIBRIUM

UR - http://www.scopus.com/inward/record.url?scp=85125097888&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e64c63a8-1188-365c-8729-b05b98ea0dc6/

U2 - 10.1007/s10957-022-02010-5

DO - 10.1007/s10957-022-02010-5

M3 - Article

AN - SCOPUS:85125097888

VL - 194

SP - 92

EP - 120

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 1

ER -