Research On Network Game Based On Bilateral Connection Rules And Its Stability

The familiar notion of Nash equilibrium is not the only conceptual stability that arises in the study of network formation.It is easy to see that the concept of Nash stability is too weak as a concept for modeling network formation when links are bilateral,as it allows for too many equilibrium networks.To overcome this type of coordination failure,the concept of pairwise stable networks becomes the complementary approach to the process of network formation.This thesis investigates the corresponding stability in the Jackson-Wolinsky network formation game,the Myerson linking game and the repeated network game with Myerson linking game in network formation stage.First of all,by establishing equivalent condition of pairwise stability networks with Jackson-Wolinsky rules,the complete algorithm is given to find pairwise stability networks,pairwise stability networks allowing for side payments when adding links and pairwise stability networks allowing for side payments when adding and deleting links.After the introduction of side payments,the set of pairwise stability networks allowing for side payments when adding links is the intersection of the set of pairwise stability networks and the set of pairwise stability networks allowing for side payments when adding and deleting links is proven.Secondly,the influence of the social network structure and the payoff function on the pairwise stability of two specific network models is analyzed systematically.The ranges of parameters when the network is pairwise stability,pairwise stability allowing for side payments when adding links or pairwise stability allowing for side payments when adding and deleting links are compared.Based on the Myerson linking game,the parameter range of pairwise Nash stability is analyzed for the specific network model.Finally,the repeated network game based on strategic interaction with Myerson linking game in network formation stage is investigated,taking Shapley value as cooperative solution.In order to ensure the stability of cooperation,the time consistent imputation distribution procedure of Shapley value is designed,the asynchronous irrational behavior proof condition is studied,and an example is given to satisfy the asynchronous irrational behavior proof condition.