Social Network Analysis

This page contains recent working papers on network formation and the game theoretic network analysis.

Middleman and Contestation in Directed Networks

by Owen Sims and Robert P. Gilles

January 2017


This paper studies middlemen that act as critical intermediators of flows in a directed network. The contestability of an arbitrary intermediary node is introduced as a network topological concept of competitiveness meaning that an intermediary’s role in the brokering of flows in the network can be substituted by a group of other nodes. We establish the equivalence of uncontested intermediaries and middlemen.

The notion of contestation gives rise to a measure that quantifies the control exercised by a middleman in a network. We present a comparison of this middleman centrality measure with relevant, established network centrality measures. Furthermore, we provide concepts and measures expressing the robustness of a middleman as the number of links or nodes that have to be added to or removed from the network to nullify the middleman’s power.

We use these concepts to study middleman power and robustness in two empirical networks: Krackhardt’s advice network of managers in a medium-sized corporation and the well-known Florentine marriage network.

PDF file of this paper: CNodes-2017

ArXiV version of current draft (December 2016)

ArXiv version of previous draft (January 2014).

Platform Competition as Network Contestability

by Robert P. Gilles and Dimitrios Diamantaras

October 2013; Revised: January 2014

Recent research in industrial organisation has investigated the essential place that middlemen have in the networks that make up our global economy. In this paper we attempt to understand how such middlemen compete with each other through a game theoretic analysis using novel techniques from decision-making under ambiguity.

We model a purposely abstract and reduced model of one middleman who provides a two-sided platform, mediating surplus-creating interactions between two users. The middleman evaluates uncertain outcomes under positional ambiguity, taking into account the possibility of the emergence of an alternative middleman offering intermediary services to the two users.

Surprisingly, we find many situations in which the middleman will purposely extract maximal gains from her position. Only if there is relatively low probability of devastating loss of business under competition, the middleman will adopt a more competitive attitude and extract less from her position.

January 2014 version of this paper: NetComp2014

ArXiv version of this paper (October 2013).

Network Formation under Mutual Consent and Costly Communication

by Robert P. Gilles and Sudipta Sarangi

October 2009;    Published: 2010

We consider two different approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider a network-based approach; in particular Jackson-Wolinsky’s concept of pairwise stability. Next, we discuss a non-cooperative game-theoretic approach, through a refinement of the Nash equilibria of Myerson’s consent game. This refinement, denoted as monadic stability, describes myopically forward looking behavior of the players. We show through an equivalence that the class of monadically stable networks is a strict subset of the class of pairwise stable network that can be characterized fully by modifications of the properties defining pairwise stability.

October 2009, extended version of the paper: Gilles-Sarangi (2009)

The published version of this paper can be found at the web site of Mathematical Social Sciences.

Evolution of Conventions in Endogenous Social Networks

by Edward Droste, Robert P. Gilles and Cathleen Johnson

April 2000

We analyze the dynamic implications of learning in a large population coordination game where both the actions of the players and the communication network evolve over time. Cost considerations of social interaction are incorporated by considering a circular model with endogenous neighborhoods, meaning that the locations of the players are fixed but players can create their own communication network.
The dynamic process describing medium-run behavior is shown to converge to an absorbing state, which may be characterized by coexistence of conventions. In the long run, when mistake probabilities are small but nonvanishing, coexistence of conventions is no longer sustainable as the risk-dominant convention becomes the unique stochastically stable state.

PDF file of this paper: DGJ (2000)

Updated: 2016-12-30