This page contains recent working papers on game theoretic models of network formation, the analysis of network games, the allocation of collectively generated wealth in a social network, and game theoretic social network analysis.
Game theoretic foundations of the Gately power measure for directed networks
by Robert P. Gilles and Lina Mallozzi
August 2023
Abstract:
We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the 𝛽-measure, and construct an axiomatisation of the Gately measure.
Paper has been published in Games
This paper is available from ArXiV at 2308.02274.
Expected Values for Variable Network Games
by Subhadip Chakrabarti, Loyimee Gogoi, Robert P. Gilles, Surajit Borkotokey, and Rajnish Kumar
August 2021 – Revised: May 2023
A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting.
We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatisations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatisation of the Position Value based on the balanced link contribution property to the Expected Position Value.
Published online in Annals of Operations Research.
The paper is available from ArXiV: 2108.07047
Probabilistic Network Values
by Surajit Borkotokey, Subhadip Chakrabarti, Robert P. Gilles, Loyimee Gogoi, and Rajnish Kumar
October 2019 – Revised: May 2021
Abstract:
We consider a class of cooperative network games with transferable utilities in which players interact through a probabilistic network rather than a regular, deterministic network. In this class of wealth-generating situations we consider probabilistic extensions of the Myerson value and the position value. For the subclass of probabilistic network games in multilinear form, we establish characterizations of these values using an appropriate formulation of component balancedness. We show axiomatizations based on extensions of the well-accepted properties of equal bargaining power, balanced contributions, and balanced link contributions.
Published in Mathematical Social Sciences
Building social networks under consent: A survey
by Robert P. Gilles
October 2019 – Revised: April 2020
Abstract:
This survey explores the literature on game-theoretic models of network formation under the hypothesis of mutual consent in link formation. The introduction of consent in link formation imposes a coordination problem in the network formation process. This survey explores the conclusions from this theory and the various methodologies to avoid the main pitfalls.
The main insight originates from Myerson’s work on mutual consent in link formation and his main conclusion that the empty network (the network without any links) always emerges as a strong Nash equilibrium in any game-theoretic model of network formation under mutual consent and positive link formation costs.
Jackson and Wolinsky introduced a cooperative framework to avoid this main pitfall. They devised the notion of a pairwise stable network to arrive at equilibrium networks that are mainly non-trivial. Unfortunately, this notion of pairwise stability requires coordinated action by pairs of decision makers in link formation.
I survey the possible solutions in a purely non-cooperative framework of network formation under mutual consent by exploring potential refinements of the standard Nash equilibrium concept to explain the emergence of non-trivial networks. This includes the notions of unilateral and monadic stability. The first one is founded on advanced rational reasoning of individuals about how others would respond to one’s efforts to modify the network. The latter incorporates trusting, boundedly rational behaviour into the network formation process. The survey is concluded with an initial exploration of external correlation devices as an alternative framework to address mutual consent in network formation.
ArXiV version of the current draft
Middleman and Contestation in Directed Networks
by Owen Sims and Robert P. Gilles
January 2017
Abstract:
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.
ArXiV version of current draft (December 2016)
ArXiv version of a previous draft (January 2014).
Platform Competition as Network Contestability
by Robert P. Gilles and Dimitrios Diamantaras
October 2013 – Revised: January 2014
Abstract:
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.
ArXiv version of this paper (October 2013).
Network Formation under Mutual Consent and Costly Communication
by Robert P. Gilles and Sudipta Sarangi
October 2009
Abstract:
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.
Published in Mathematical Social Sciences
October 2009, extended version of the paper: Gilles-Sarangi (2009)
Evolution of Conventions in Endogenous Social Networks
by Edward Droste, Robert P. Gilles and Cathleen Johnson
April 2000
Abstract:
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.