A strategic model for network formation

Abstract

We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for game-theoretic network formation models in which links are formed due to strategic behaviors of individuals rather than based on probabilities. Inspired by Even-Dar and Kearns' model (NIPS 19: 385-392, 2007), we consider a more realistic framework in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation and maintenance of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most four in the general set of equilibrium networks in our model. We achieved an economic mechanism and its dynamic process for individuals which firstly, unlike the earlier model, the outcomes of players' interactions or the equilibrium networks are guaranteed to exist. Furthermore, these networks coincide with the outcome of pairwise Nash equilibrium in network formation. Secondly, it generates large-scale networks that have a rational and strategic microfoundation and demonstrate the main characterization of small degree of separation in real-life social networks. Moreover, we provide a network formation simulation that generates small-world networks.

The winner takes it all—Competitiveness of single nodes in globalized supply networks

“…However, neither model class fully describes socio-economic networks, whose formation is determined by the individual decisions (optimization, non-random) of interacting agents (multiple different objective functions). Economic equilibrium models and game-theoretic models capture these interactions and the individual decision but quickly become intractable as the number of agents increases [3, 24–28].…”

A hierarchical network formation model

“…4 They showed the appearance of small diameter link stable networks within the threshold of α = 2. Further, Atabati and Farzad [1] expand this result by showing the existence of a small diameter in the general set of equilibrium networks under the new assumption of dynamic link-pricing that better represents the dynamic nature of network formation.…”

“…Moreover, c ij , as it is introduced in [1], illustrates the fixed maintenance cost of link ij in which both i and j should consider this charge for maintaining their links at each of point of analysis during the game. In addition, the process of network formation is defined in terms of improving paths.…”

Two-stage network games modeling the Belt and Road Initiative

“…In the work [7] a dynamic network formation game with incomplete information is proposed where players do not know the players' types beforehand, but have to learn through the dynamics. And in the work [8] the dynamics of a network formation model are concerned and it is proved that the set of pairwise stable networks coincides with the set of pairwise Nash stable networks.…”