The Time-Consistent Shapley Value for Two-Stage Network Games with Pairwise Interactions

2018 ◽  
pp. 15-23
Author(s):  
Leon Petrosyan ◽  
Mariia Bulgakova ◽  
Artem Sedakov
Keyword(s):  
Shapley Value ◽  
Two Stage ◽  
Network Games ◽  
Pairwise Interactions

scholarly journals Non-Zero Sum Network Games with Pairwise Interactions

2021 ◽  
Vol 14 ◽  
pp. 38-48
Author(s):  
Mariia A. Bulgakova ◽  
Keyword(s):  
Shapley Value ◽  
Network Formation ◽  
Network Games ◽  
Zero Sum Games ◽  
Pairwise Interactions ◽  
Formation Stage ◽  
The Shapley Value ◽  
Cooperative Solutions ◽  
Zero Sum ◽  
Network Form

In the paper non-zero sum games on networks with pairwise interactions are investigated. The first stage is network formation stage, where players chose their preferable set of neighbours. In all following stages simultaneous non-zero sum game appears between connected players in network. As cooperative solutions the Shapley value and τ -value are considered. Due to a construction of characteristic function both formulas are simpli ed. It is proved, that the coeffcient λ in τ -value is independent from network form and number of players or neighbours and is equal to 1/2 . Also it is proved that in this type of games on complete network the Shapley value and τ -value are coincide.

scholarly journals Dynamic cooperative network games with pairwise interactions

2020 ◽  
Vol 13 ◽  
pp. 95-120
Author(s):  
Mariia A. Bulgakova ◽  
Keyword(s):  
Dynamic Network ◽  
Pairwise Interaction ◽  
Cooperative Network ◽  
Two Stage ◽  
Network Games ◽  
Pairwise Interactions

This article is an overview of results obtained in the field of dynamic network games with pairwise interaction. The paper provides a summary and analysis of works related to two-stage and multistage nonzero-sum games based on pairwise interaction. The meaning of pairwise interaction is to consider the game as a family of games occurring on a network between pairs of players (vertices of a graph) connected to each other by an edge. The network can be set or formed in the first stage. In the paper, solutions of cooperative pairwise interaction games are also considered.

scholarly journals Strongly Time-consistent Solutions for Two-stage Network Games

2014 ◽  
Vol 31 ◽  
pp. 255-264 ◽  
Author(s):  
Hongwei Gao ◽  
Leon Petrosyan ◽  
Artem Sedakov
Keyword(s):  
Two Stage ◽  
Network Games

Two-stage network games

2016 ◽  
Vol 77 (10) ◽  
pp. 1855-1866 ◽  
Author(s):  
L. A. Petrosyan ◽  
A. A. Sedakov ◽  
A. O. Bochkarev
Keyword(s):  
Two Stage ◽  
Network Games

Trade with Technology Spillover: A Dynamic Network Game Analysis

2020 ◽  
pp. 2050011
Author(s):  
David W. K. Yeung ◽  
Leon A. Petrosyan ◽  
Yingxuan Zhang
Keyword(s):  
Shapley Value ◽  
General Class ◽  
Dynamic Network ◽  
Technology Spillover ◽  
Network Games ◽  
Game Analysis ◽  
The Shapley Value ◽  
Positive Externalities ◽  
Network Game ◽  
Representative Model

This paper presents a general class of dynamic network games to analyze trade with technology spillover. Due to the fact that the benefits of technology spillover are not fully accrued to the technology developer, the positive externalities are under-exploited. The cooperative solution yields an optimal outcome. To reflect the contributions of individual agents to the network, the Shapley value is used as a solution optimality principle in sharing the cooperative gains. A time-consistent payoff imputation procedure is derived to maintain the Shapley value at each stage of the cooperation. A representative model based on the general class of network games with explicit functional form is given. This is the first time that trade with technology spillover is studied in the framework of dynamic network games, further studies along this line are expected.

The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock

2015 ◽  
Vol 6 (4) ◽  
pp. 520-537 ◽  
Author(s):  
Leon Petrosyan ◽  
Artem Sedakov
Keyword(s):  
Shapley Value ◽  
Dynamic Network ◽  
Network Games

scholarly journals New Characteristic Function for Two Stage Games with Spanning Tree

2021 ◽  
Vol 14 ◽  
pp. 59-71
Author(s):  
Cheng Min ◽  
◽  
Li Yin ◽  
◽  
Keyword(s):  
Characteristic Function ◽  
Shapley Value ◽  
Spanning Tree ◽  
Stochastic Game ◽  
Cooperative Behaviour ◽  
Two Stage ◽  
New Approach ◽  
The Shapley Value

Two-stage n-player games with spanning tree are considered. The cooperative behaviour of players is defined. After the first stage, a specified player leaves the game with a probability that depends on the actions of all players in the first stage. A new approach to the construction of the characteristic function is proposed. In the game, all players are connected with the source directly or indirectly. Assume that the players in coalition N \ S have already connected to the source when the players in coalition S ⊂ N wish to connect to the source. The players in coalition S could connect to the source with the help of the players in coalition N \ S. A new characteristic function is de ned in the game, and the Shapley value is constructed. Several results based on the new characteristic function in the two-stage stochastic game are given.

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