A network formation game for the emergence of hierarchies

We propose a novel network formation game that explains the emergence of various hierarchical structures in groups where self-interested or utility-maximizing individuals decide to establish or severe relationships of authority or collaboration among themselves. We consider two settings: we first consider individuals who do not seek the other party’s consent when establishing a relationship and then individuals who do. For both settings, we formally relate the emerged hierarchical structures with the novel inclusion of well-motivated hierarchy promoting terms in the individuals’ utility functions. We first analyze the game via a static analysis and characterize all the hierarchical structures that can be formed as its solutions. We then consider the game played dynamically under stochastic interactions among individuals implementing better-response dynamics and analyze the nature of the converged networks.

Structural hole centrality: evaluating social capital through strategic network formation

Strategic network formation is a branch of network science that takes an economic perspective to the creation of social networks, considering that actors in a network form links in order to maximise some utility that they attain through their connections to other actors in the network. In particular, Jackson’s Connections model, writes an actor’s utility as a sum over all other actors that can be reached along a path in the network of a benefit value that diminishes with the path length. In this paper, we are interested in the “social capital” that an actor retains due to their position in the network. Social capital can be understood as an ability to bond with actors, as well as an ability to form a bridge that connects otherwise disconnected actors. This bridging benefit has previously been modelled in another “structural hole” network formation game, proposed by Kleinberg. In this paper, we develop an approach that generalises the utility of Kleinberg’s game and combines it with that of the Connections model, to create a utility that models both the bonding and bridging capabilities of an actor with social capital. From this utility and its associated formation game, we derive a new centrality measure, which we dub “structural hole centrality”, to identify actors with high social capital. We analyse this measure by applying it to networks of different types, and assessing its correlation to other centrality metrics, using a benchmark dataset of 299 networks, drawn from different domains. Finally, using one social network from the dataset, we illustrate how an actor’s “structural hole centrality profile” can be used to identify their bridging and bonding value to the network.

Stable Production Networks

One of the key features which promote growth of industrial clusters is collaboration among firms within such clusters. Collaboration among firms leads to the formation of networks. Stability of these networks is vital to the sustainability of the particular firms. In this paper, we model a supply chain network where a set of downstream firms (players) source inputs from upstream firms (players) who manufacture goods, add value to the products and resell them. The upstream firms produce identical goods and compete on quantities to sell these goods to the downstream firms. The upstream firms procure goods from the downstream firms and sell them. Additionally, upstream firms network among themselves so as to reduce their costs. We model this setting as a two-stage [Formula: see text]-player strategic network formation game. Firms decide their links before competing on quantities in the second stage of the game. Using the defined model, we derive equilibrium quantities and profits as a function of the network structure and number of firms. Following which we analyze the conditions under which different stable network emerge. Our analysis brings forth several interesting insights such as higher connections among downstream players lead to increased profits for upstream manufacturers. From the network stability perspective, we obtain the conditions under which regular, star, etc. network structures are pairwise and bilaterally stable. Furthermore, we also find the conditions under which core–periphery network structures emerge and are stable.

Network Formation under Random Attack and Probabilistic Spread

We study a network formation game where agents receive benefits by forming connections to other agents but also incur both direct and indirect costs from the formed connections. Specifically, once the agents have purchased their connections, an attack starts at a randomly chosen vertex in the network and spreads according to the independent cascade model with a fixed probability, destroying any infected agents. The utility or welfare of an agent in our game is defined to be the expected size of the agent's connected component post-attack minus her expenditure in forming connections. Our goal is to understand the properties of the equilibrium networks formed in this game. Our first result concerns the edge density of equilibrium networks. A network connection increases both the likelihood of remaining connected to other agents after an attack as well the likelihood of getting infected by a cascading spread of infection. We show that the latter concern primarily prevails and any equilibrium network in our game contains only $O(n\log n)$ edges where $n$ denotes the number of agents. On the other hand, there are equilibrium networks that contain $\Omega(n)$ edges showing that our edge density bound is tight up to a logarithmic factor. Our second result shows that the presence of attack and its spread through a cascade does not significantly lower social welfare as long as the network is not too dense. We show that any non-trivial equilibrium network with $O(n)$ edges has $\Theta(n^2)$ social welfare, asymptotically similar to the social welfare guarantee in the game without any attacks.

Competition for Status Creates Superstars: an Experiment on Public Good Provision and Network Formation

We investigate a mechanism that facilitates the provision of public goods in a network formation game. We show how competition for status encourages a core player to realize efficiency gains for the entire group. In a laboratory experiment we systematically examine the effects of group size and exogenously monetarized status rents. The experimental results provide very clear support for the concept of challenge-freeness, a refinement that predicts when a repeated game equilibrium will be played, and if so which one. Two control treatments allow us to reject the possibility that these observations are driven by social preferences, independently of the competition for status.

Homophily and Social Norms in Experimental Network Formation Games

Field studies of networks have uncovered a preference to befriend people we perceive as similar according to some dimensions of our identity (“homophily”). Lab studies of network formation games have found that adherence to social norms of reciprocity and inequity aversion are also drivers of network choices. No study so far has attempted to investigate the role of both homophily and social norms in a controlled environment. At the beginning of our experiment, each player fills in a personal profile. Each player then views the profile of all other players and expresses a degree of perceived similarity between his/her profile and the profile of the other player. At this point, a repeated network formation game ensues. We find that: (1) potential homophily considerations triggered by the profile rating task did not measurably change the players’ behavior compared to the baseline; (2) reciprocity plays a significant role in the formulation of the players’ strategies, in particular lowering the probability that the player naively best responds to the network observed in the previous period. We speculate that reciprocation of past choices might be a more “available” aid in strategy-formulation than considerations related to the similarity of the other players.