
on Network Economics 
By:  Rahmi Ilkiliç (Maastricht University) 
Abstract:  Suppose markets and firms are connected in a bipartite network, where firms can only supply to the markets they are connected to. Firms compete a la Cournot and decide how much to supply to each market they have a link with. We assume that markets have linear demand functions and firms have convex quadratic cost functions. We show there exists a unique equilibrium in any given network of firms and markets. We provide a formula which expresses the quantities at an equilibrium as a function of a network centrality measure. 
Keywords:  Cournot Markets, Networks, Nash Equilibrium, Centrality Measures 
JEL:  C62 C72 D85 L11 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.32&r=net 
By:  Edoardo Gallo (University of Oxford) 
Abstract:  Many social networks have the following properties: (i) a short average distance between any two individuals; (ii) a high clustering coefficient; (iii) segregation patterns; the presence of (iv) brokers and (v) hubs. (i) and (ii) define a small world network. This paper develops a strategic network formation model where agents have heterogeneous knowledge of the network: cognizant agents know the whole network, while ignorant ones are less knowledgeable. For a broad range of parameters, all pairwise Nash (PN) networks have properties (i)(iv). There are some PN networks with one hub. Cognizant agents have higher betweenness centrality: they are the brokers who connect different parts of the network. Ignorant agents cause the emergence of segregation patterns. The results are robust to varying the number of cognizant agents and to increasing the knowledge level of ignorant ones. An application shows the relevance of the results to assessing the welfare impact of an increase in network knowledge due to, e.g., improved access to social networking tools. 
Keywords:  Network, Cognitive Network, Small World, Broker, Segregation 
JEL:  C72 D85 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.34&r=net 
By:  Frank H. Page (Indiana University); Myrna H. Wooders 
Abstract:  In all social and economic interactions, individuals or coalitions choose not only with whom to interact but how to interact, and over time both the structure (the “with whom”) and the strategy (“the how”) of interactions change. Our objectives here are to model the structure and strategy of interactions prevailing at any point in time as a directed network and to address the following open question in the theory of social and economic network formation: given the rules of network and coalition formation, the preferences of individuals over networks, the strategic behavior of coalitions in forming networks, and the trembles of nature, what network and coalitional dynamics are likely to emerge and persist. Our main contributions are (i) to formulate the problem of network and coalition formation as a dynamic, stochastic game, (ii) to show that this game possesses a stationary correlated equilibrium (in network and coalition formation strategies), (iii) to show that, together with the trembles of nature, this stationary correlated equilibrium determines an equilibrium Markov process of network and coalition formation, and (iv) to show that this endogenous process possesses a finite, nonempty set of ergodic measures, and generates a finite, disjoint collection of nonempty subsets of networks and coalitions, each constituting a basin of attraction. We also extend to the setting of endogenous Markov dynamics the notions of pairwise stability (JacksonWolinsky, 1996), strong stability (Jacksonvan den Nouweland, 2005), and Nash stability (BalaGoyal, 2000), and we show that in order for any networkcoalition pair to persist and be stable (pairwise, strong, or Nash) it is necessary and sufficient that the pair reside in one of finitely many basins of attraction. The results we obtain here for endogenous network dynamics and stochastic basins of attraction are the dynamic analogs of our earlier results on endogenous network formation and strategic basins of attraction in static, abstract games of network formation (Page and Wooders, 2008), and build on the seminal contributions of Jackson and Watts (2002), Konishi and Ray (2003), and Dutta, Ghosal, and Ray (2005). 
Keywords:  Endogenous Network Dynamics, Dynamic Stochastic Games of Network Formation, Equilibrium Markov Process of Network Formation, Basins of Attraction, Harris Decomposition, Ergodic Probability Measures, Dynamic Path Dominance Core, Dynamic Pairwise Stability 
JEL:  A14 C71 C72 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.28&r=net 
By:  Markus Kinateder (Universidad de Navarra) 
Abstract:  Two project leaders (or entrepreneurs) in a network, which captures social relations, recruit players in a strategic, competitive and timelimited process. Each team has an optimal size depending on the project’s quality. This is a random variable with a commonly known distribution. Only the corresponding project leader observes its realization. Any decision is only observed by the involved agents. The set of pure strategy Sequential Equilibria is characterized by giving an algorithm that selects one equilibrium at a time. An agent’s expected payoff is related to his position in the network, though no centrality measure in the literature captures this relation. A social planner frequently would achieve a higher welfare. 
Keywords:  Dynamic Competitive Group Formation, Imperfect Information 
JEL:  C72 C73 D85 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.36&r=net 
By:  Pollitt, M.G. 
Abstract:  The purpose of this paper is to examine the lessons from the recent history of telecoms deregulation for the electricity (and by implication heat) network regulation. We do this in the context of Ofgem’s RPIX@ 20 Review of energy regulation in the UK, which considers whether RPIX based price regulation is fit for purpose after over 20 years of operation in energy networks. We examine the deregulation of fixed line telecoms in the UK and the lessons which it seems to suggest. We then apply the lessons to electricity networks in the context of a possible increase in distributed generation directly connected to local distribution networks. We conclude that there is the possibility of more parallels over time and suggest several implications of this for the regulation of electricity and heat networks. 
Keywords:  electricity, network regulation, distributed generation 
JEL:  L51 L98 
Date:  2009–06–09 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:0925&r=net 
By:  Benjamin Golub (Stanford University); Matthew O. Jackson (Stanford University) 
Abstract:  We examine how three different communication processes operating through social networks are affected by homophily  the tendency of individuals to associate with others similar to themselves. Homophily has no effect if messages are broadcast or sent via shortest paths; only connection density matters. In contrast, homophily substantially slows learning based on repeated averaging of neighbors' information and Markovian diffusion processes such as the Google random surfer model. Indeed, the latter processes are strongly affected by homophily but completely independent of connection density, provided this density exceeds a low threshold. We obtain these results by establishing new results on the spectra of large random graphs and relating the spectra to homophily. We conclude by checking the theoretical predictions using observed high school friendship networks from the Adolescent Health dataset. 
Keywords:  Networks, Learning, Diffusion, Homophily, Friendships, Social Networks, Random Graphs, Mixing Time, Convergence, Speed of Learning, Speed of Convergence 
JEL:  D83 D85 I21 J15 Z13 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.35&r=net 
By:  Vincent Vannetelbosch (CORE, Université catholique de Louvain); JeanFrançois Caulier (Universitaires SaintLouis); Ana Mauleon (FNRS and CEREC, CORE, Université catholique de Louvain) 
Abstract:  We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the componentwise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and efficiency. 
Keywords:  Networks, Coalition Structures, Contractual Stability, Allocation Rules 
JEL:  A14 C70 
Date:  2009–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.47&r=net 
By:  Tim Hellmann (Bielefeld University); Berno Buechel (Bielefeld University) 
Abstract:  Since the seminal contribution of Jackson & Wolinsky 1996 [A Strategic Model of Social and Economic Networks, JET 71, 4474] it has been widely acknowledged that the formation of social networks exhibits a general conflict between individual strategic behavior and collective outcome. What has not been studied systematically are the sources of inefficiency. We approach this omission by analyzing the role of positive and negative externalities of link formation. This yields general results that relate situations of positive externalities with stable networks that cannot be “too dense” in a welldefined sense, while situations with negative externalities tend to induce “too dense” networks. 
Keywords:  Networks, Network Formation, Connections, Game Theory, Externalities, Spillovers, Stability, Efficiency 
JEL:  D85 C72 L14 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.38&r=net 
By:  Francesco Feri; Miguel A.MeléndezJiménez 
Abstract:  This paper studies an evolutionary model of network formation with endogenous decay, in which agents benefit both from direct and indirect connections. In addition to forming (costly) links, agents choose actions for a coordination game that determines the level of decay of each link. We address the issues of coordination (longrun equilibrium selection) and network formation by means of stochastic stability techniques. We find that both the link cost and the tradeoff between efficiency and riskdominance play a crucial role in the longrun behavior of the system. 
Keywords:  Coordination, Networks, Risk dominance, stochastic stability 
JEL:  C72 C73 D83 D85 
Date:  2009–07 
URL:  http://d.repec.org/n?u=RePEc:inn:wpaper:200919&r=net 
By:  Dotan Persitz (Tel Aviv University) 
Abstract:  The heterogeneous connections model is a generalization of the homogeneous connections model of Jackson and Wolinsky (1996) in which the intrinsic value of each connection is set by a discrete, positive and symmetric function that depends solely on the types of the two end agents. Core periphery networks are defined as networks in which the agents' set can be partitioned into two subsets, one in which the members are completely connected among themselves and the other where there are no internal links. A twotype society is defined as "power based" if both types of agents prefer to connect to one of the types over the other, controlling for path length. An exhaustive analysis shows that core periphery networks, in which the "preferred" types are in the core and the "rejected" types are in the periphery, are crucial in the "power based" society. In particular, if the linking costs are not too low and not too high, at least one such network is pairwise stable. Moreover, in many cases these networks are the unique pairwise stable networks and in all cases they are the unique strongly efficient networks. The set of efficient networks often differs from the set of pairwise stable networks, hence a discussion on this issue is developed. These results suggest heterogeneity accompanied by "power based" linking preferences as a natural explanation for many coreperiphery structures observed in real life social networks. 
Keywords:  Network Formation, Heterogeneity, Pairwise Stability 
JEL:  D85 L14 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.42&r=net 
By:  Marc Kilgour (Wilfrid Laurier University); Steven J. Brams (New York University) 
Abstract:  Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players common to them, or kingmakers, determine which fallback coalition will form. The players(s) who are the first to be acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumptions—particularly, different kinds of singlepeakedness—and of player weights on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them. 
Keywords:  Coalition, Fallback Process, Kingmaker Leader, Cardinally Singlepeaked, Ordinally Singlepeaked 
JEL:  C71 C78 D72 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2009.41&r=net 