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We analyze reciprocal market sharing agreements by which firms commit not to enter each other's territory in oligopolistic markets and procurement auctions. The set of market sharing agreements defines a collusive network. We characterize stable collusive networks when firms and markets are symmetric. Stable networks are formed of complete alliances, of different sizes, larger than a minimal threshold. Typically, stable networks display fewer agreements than the optimal network for the industry and more agreements than the socially optimal network. When firms or markets are asymmetric, stable networks may involve incomplete alliances and be underconnected with respect to the social optimum. Copyright 2004 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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... Theoretical results on the structural properties of communities were obtained in the context of network formation games [6,7,8,9,10,11]. Jackson and Wolinsky presented one of the first, and most influential, analysis of network formation games [9]. ...

... We first establish Eq. (8). Using the definition of G(Λ), we rewrite G((µ ′ c , Λ p ))− G((µ ′′ c , Λ p )) as . ...

... Next, we establish Eq. (8). We obtain that ...

It has been experimentally shown that communities in social networks tend to have a core-periphery topology. However, there is still a limited understanding of the precise structure of core-periphery communities in social networks including the connectivity structure and interaction rates between agents. In this paper, we use a game-theoretic approach to derive a more precise characterization of the structure of core-periphery communities.

... In recent years, the globalization of markets and the deregulation of industries which used to be regulated on a territorial basis (airlines, local telecommunication services and utilities) have increased the scope for explicit or implicit market sharing agreements (Belleflamme and Bloch, 2004). The antitrust authorities started to emphasize market sharing agreements as an alternative form of collusion which limits competition in the product market. ...

... Our results are similar to Goyal and Moraga-Gonzalez (2001) since we show that there is an intermediate level of connectivity which maximizes industry profits when there are R&D spillovers. Last but not the least, market sharing agreements are studied by Belleflamme and Bloch (2004) who characterize stable collusive networks in oligopolistic markets with symmetric firms and identical markets. The authors show that in a stable network firms form complete components and give an explicit formula for the minimal size of the component. ...

The paper aims at analyzing the R&D incentives of oligopolistic firms pro-ducing homogeneous products in a collusive network where they can form recip-rocal market sharing agreements. These agreements refrain firms from entering each other's market decreasing the level of competition in home market and at the same time reducing the number of foreign markets they can enter. We will analyze the effect of the level of competition (captured by the number of collusive agreements) on R&D incentives of firms with and in absence of R&D spillovers among connected firms. We develop a model to examine the architecture of strategically stable networks and the relation between individual incentives and social welfare in networks. The first results suggest that when there are no R&D collaborations among firms, R&D effort level of an individual firm decreases as the number of collusive agreements increases. Along with the connectivity in the network, the profits increase at the expense of consumers resulting in an intermediate level of com-petition that maximizes the social welfare. When firms undertake collaborative R&D and collude in the market stage by not entering each other's market, we show that some intermediate level of collaboration is optimal for total R&D, profits and efficiency. We show that given the collaborative and market shar-ing agreements, the complete network is stable while the stability of the empty network depends on the number of markets and the level of R&D spillovers.

... The supply and demand functions then induce a value function and allocation rules over the countries. Belleflamme and Bloch [15] model market sharing between firms where a link between two firms represents an agreement not to infringe on each other's market and the absence of a link implies the firms will compete in the same market. Again, supply and demand induce a value function and an allocation rule over the firms. ...

... Jackson notes that pairwise stability may be too weak because it does not allow groups of players to add or delete links, only pairs of players [18]. Deletion of multiple links simultaneously has been considered in [15]. ...

As an alternative view to the graph formation models in the statistical
physics community, we introduce graph formation models using \textit{network
formation} through selfish competition as an approach to modeling graphs with
particular topologies. We further investigate a specific application of our
results to collaborative oligopolies. We extend the results of Goyal and Joshi
(S. Goyal and S. Joshi. Networks of collaboration in oligopoly. Games and
Economic behavior, 43(1):57-85, 2003), who first considered the problem of
collaboration networks of oligopolies and showed that under certain linear
assumptions network collaboration produced a stable complete graph through
selfish competition. We show with nonlinear cost functions and player payoff
alteration that stable collaboration graphs with an arbitrary degree sequence
can result.

... L'impresa sceglierà la struttura di relazioni (linking) più profittevole e l'interazione strategica fra imprese porterà a definire quali networks possono considerarsi di equilibrio e quali no. Esempi di networks si ritrovano negli accordi di reciproca spartizione del mercato oppure in quelli di cross licensing per l'utilizzo reciproco di brevetti (Belleflamme, Bloch, 2004). ...

Il lavoro studia il contratto di rete, introdotto in Italia nel 2009, inquadrandolo fra le modalità di interazione formale fra le imprese. Tale strumento risponde a un’esigenza di flessibilità degli operatori, non soddisfatta dalle forme tradizionali di coordinamento; tuttavia, l’indeterminatezza dei suoi contenuti, rimessi alla volontà delle parti, può ridurre l’affidabilità dello strumento nei rapporti con i terzi: benefici sotto tale profilo potrebbero derivare da una standardizzazione dei contenuti, non vincolante, volta ad orientare gli operatori verso modelli più efficienti, accrescendone l’utilità. Il contratto di rete, inoltre, si inserisce in un quadro frammentario di incentivi fiscali analoghi nelle finalità ma rivolti a varie forme di coordinamento, che possono distorcere le scelte degli operatori. Ai nuovi contratti di rete hanno aderito imprese che avevano spesso rapporti preesistenti e localizzate in regioni ad alta intensità distrettuale; tuttavia, i confini territoriali delle reti sono di frequente più ampi dei tradizionali distretti. La probabilità che un’impresa aderisca a una rete è positivamente correlata con la dimensione e la crescita e negativamente con la redditività.

... This concept of link deletion proofness, similar to stable networks (Watts, 2001) and pairwise stability (Jackson and Wolinsky, 1996), concerns only a single change in the network at once. A stability concept that allows players to delete any set of links at once is called strong link deletion proofness (Gilles and Sarangi, 2004;Belleflamme and Bloch, 2004). Definition: R is strong link deletion proof in a given , ...

Network models of collective action commonly assume fixed social networks in which ties influence participation through social rewards. This implies that only certain ties are beneficial from the view of individual actors. Accordingly, in this study we allow that actors strategically revise their relations. Moreover, in our model actors also take into account possible network consequences in their participation choices. To handle the interrelatedness of networks and participation, we introduce new equilibrium concepts. Our equilibrium analysis suggests that structures that tend to segregate contributors from free riders are stable, but costless network change only promotes all-or-nothing participation and complete networks.

... Jackson notes that pairwise stability may be too weak because it does not allow groups of players to add or delete links, only pairs of players Jackson (2003). Deletion of multiple links simultaneously has been considered in Belleflamme and Bloch (2004). We present an application of the network formation game to firm collaboration in spatial oligopolies, which is an extension to the firm collaboration presented by Goyal and Joshi in Goyal and Joshi (2003).Furthermore, we define the degree sequence based on Melnikov et al. (1998) as follows: ...

Recently, it has been shown that networks with an arbitrary degree sequence may be a stable solution to a network formation game. Further, in recent years there has been a rise in the number of firms participating in collaborative efforts. In this paper, we show conditions under which a graph with an arbitrary degree sequence is admitted as a stable firm collaboration graph.

... In recent years, a number of studies have examined the empirical properties of the world wide web, citation networks, and telephone calling. 13 This work has highlighted the following features: the average number of connections is typically very small as compared to the number of nodes, the average distance between players is very small, and there is significant inequality in the number of connections across players. It is natural to ask if the theoretical findings are consistent with these empirical regularities. ...

... Here, I provide a noncooperative grounding of weakly pairwise Nash stable networks and thereby address the issue of their existence. The prior literature on network formation that uses pairwise stability or closely related concepts and addresses existence issues has either focused on establishing conditions that guarantee existence or shown existence in special settings (see e.g., Belleflamme and Bloch, 2004; Calvó-Armengol, 2004; Goyal and Joshi, 2006; Jackson and Watts, 2001). A novelty in this paper is that it presents a way to incorporate mixed strategies into a network formation game with coordinated moves. ...

This paper defines a modified version of Myerson's linking game and shows that the set of weakly pairwise Nash stable networks is characterized by the set of networks aris-ing from pure strategy Nash equilibria of this game. The game, called the linking game with player pairs, has a well-defined strategic form, and therefore the characterization allows to introduce mixed strategies to the network formation game. In addition, it is shown that weakly pairwise Nash stable networks result from the subgame-perfect Nash equilibrium in undominated strategies of a two-stage network formation game. In the first stage of this game, players can form potential links with each other. A pair of players that has formed a potential link can coordinate to form a link in the second stage.

... Jackson notes that pairwise stability may be too weak because it does not allow groups of players to add or delete links, only pairs of players [10]. Deletion of multiple links simultaneously has been considered in Belleflamme and Bloche [3]. Previously, in [13] we extend work [11] and [8] ...

We model the formation of networks as the result of a game where by players
act selfishly to get the portfolio of links they desire most. The integration
of player strategies into the network formation model is appropriate for
organizational networks because in these smaller networks, dynamics are not
random, but the result of intentional actions carried through by players
maximizing their own objectives. This model is a better framework for the
analysis of influences upon a network because it integrates the strategies of
the players involved. We present an Integer Program that calculates the price
of anarchy of this game by finding the worst stable graph and the best
coordinated graph for this game. We simulate the formation of the network and
calculated the simulated price of anarchy, which we find tends to be rather
low.

... Jackson notes that pairwise stability may be too weak because it does not allow groups of players to add or delete links, only pairs of players [12]. Deletion of multiple links simultaneously has been considered in [1]. We present an application of the network formation game to firm collaboration in spatial oligopolies, which is an extension to the firm collaboration presented by Goyal and Joshi in [4]. ...

Recently, it has been shown that networks with an arbitrary degree sequence
may be a stable solution to a network formation game. Further, in recent years
there has been a rise in the number of firms participating in collaborative
efforts. In this paper, we show conditions under which a graph with an
arbitrary degree sequence is admitted as a stable firm collaboration graph.

... In this note, we use essentially the same model as their model with four countries, and investigate which network is more likely to be realized than others by considering a dynamic process introduced by Jackson and Watts (2002). 1 ...

Goyal and Joshi (2006, Int Econ Review) apply the notion of ``pairwise stable networks" introduced by Jackson and Wolinsky (1996, J Econ Theory) to a model of free trade network formation, and show that (i) every pairwise stable network is either complete or almost complete (with all countries except one forming direct links), and (ii) the complete network maximizes global welfare. In this note, we use essentially the same model as their model with four countries, and investigate which network is more likely to be realized than others by considering a dynamic process introduced by Jackson and Watts (2002, J Econ Theory).

... We do not focus on papers which look at applications (Belleflamme and Bloch 2004;Goyal and Joshi 2006a;Furusawa and Konishi 2007;Bala and Goyal 2000b;Goyal and Moraga-González 2001;Goyal and Joshi 2003;Zirulia 2006;Suijs et al. 2005;Skorin-Kapov 2017) or touch on other tangential topics. For example, anti-coordination among agents (Bramoullé et al. 2004); contextual and correlated peer effects (Bramoullé et al. 2009); partner heterogeneity (Billand et al. 2011); and Nash and stable characterisation for a graph structure (Bramoullé et al. 2014). ...

Social storage systems are a good alternative to existing data backup systems of local, centralized, and P2P backup. Till date, researchers have mostly focussed on either building such systems by using existing underlying social networks (exogenously built) or on studying quality of service related issues. In this paper, we look at two untouched aspects of social storage systems. One aspect involves modelling social storage as an endogenous social network, where agents themselves decide with whom they want to build data backup relation, which is more intuitive than exogenous social networks. The second aspect involves studying the stability of social storage systems, which would help reduce maintenance costs and further, help build efficient as well as contented networks. We have a four fold contribution that covers the above two aspects. We, first, model the social storage system as a strategic network formation game. We define the utility of each agent in the network under two different frameworks, one where the cost to add and maintain links is considered in the utility function and the other where budget constraints are considered. In the context of social storage and social cloud computing, these utility functions are the first of its kind, and we use them to define and analyse the social storage network game. Second, we propose the concept of bilateral stability which refines the pairwise stability concept defined by Jackson and Wolinsky (J Econ Theory 71(1):44–74, 1996), by requiring mutual consent for both addition and deletion of links, as compared to mutual consent just for link addition. Mutual consent for link deletion is especially important in the social storage setting. The notion of bilateral stability subsumes the bilateral equilibrium definition of Goyal and Vega-Redondo (J Econ Theory 137(1):460–492, 2007). Third, we prove necessary and the sufficient conditions for bilateral stability of social storage networks. For symmetric social storage networks, we prove that there exists a unique neighborhood size, independent of the number of agents (for all non-trivial cases), where no pair of agents has any incentive to increase or decrease their neighborhood size. We call this neighborhood size as the stability point. Fourth, given the number of agents and other parameters, we discuss which bilaterally stable networks would evolve and also discuss which of these stable networks are efficient—that is, stable networks with maximum sum of utilities of all agents. We also discuss ways to build contented networks, where each agent achieves the maximum possible utility.

... Goyal and Joshi (2003) employ the same solution concept in a model of oligopolistic competition between firms linked in a network.Belleflamme and Bloch (2004) and Calvó-Armengol and Zenou (2004) take a similar approach but consider pairwise Nash equilibrium instead of pairwise stability as the solution concept for network formation in the first stage.13 If we instead employ pairwise Nash equilibrium as the solution concept for the first stage, we should check that no player has an incentive t ...

This paper models conflict as a contest within a network of friendships and enmities. We assume that each player is either in a friendly or in an antagonistic relation with every other player and players compete for winning by exerting costly efforts. We axiomatically characterize a success function which determines the win probability of each player given the efforts and the network of relations. In an extension, we allow for varying intensities of friendships and enmities. This framework allows for the study of strategic incentives and friendship formation under conflict as well as the application of stability concepts of network theory to contests.

... Furusawa and Konishi (2007) analyze a free trade network model, which treats the bilateral trade agreement between two countries as a link in the free trade network. Belleflamme and Bloch (2004) study a model where companies may sign bilateral market sharing agreements to form a collusive network. Corominas-Bosch (2004) and Kranton and Minehart (2001) examine the market of an indivisible good where the buyers and the sellers trade on some network structures. ...

We analyze a loan game where identical lenders and identical borrowers first form a loan network by creating bilateral links and then trade in this network. To predict the outcome of the loan game, we make two important assumptions: (i) players trade and split the surplus according to the Myerson value in any given loan network, and (ii) certain networks–networks that are pairwise stable and/or efficient under the Myerson value–are more likely to be formed. Two basic network structures, direct networks and star networks, are common in reality and sometimes coexist in a loan market. We explain these phenomena by showing that, if the link cost of each trade is small enough, these two networks are both efficient and internally stable, but they are not necessarily externally stable.

... However, we argue that there are many such contexts, and we can easily find examples in the literature on strategic network formation that satisfy this property. Among them are "Provision of a pure public good" (Goyal and Joshi, 2006a), "Market sharing agreements" (Belleflamme and Bloch, 2004), and the "Connections model" (Jackson and Wolinsky, 1996), which we discuss below. In case of a utility function that is additive separable into costs and benefits (where costs only depend on own degree), positive externalities are implied by a simple monotonicity property of the benefit function. ...

Since the seminal contribution of Jackson & Wolinsky 1996 [A Strategic Model of Social and Economic Networks, JET 71, 44-74] 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 well-defined sense, while situations with negative externalities tend to induce 'too dense' networks.

In this paper we study, as in Jeon-Menicucci (2009), competition between sellers when each of them sells a portfolio of distinct products to a buyer having limited slots. This paper considers sequential pricing and complements our main paper (Jeon- Menicucci, 2009) that considers simultaneous pricing. First, Jeon-Menicucci (2009) find that under simultaneous individual pricing, equilibrium often does not exist and hence the outcome is often inefficient. By contrast, equilibrium always exists under sequential individual pricing and we characterize it in this paper. We find that each seller faces a trade-off between the number of slots he occupies and surplus extraction per product, and there is no particular reason that this leads to an efficient allocation of slots. Second, Jeon Menicucci (2009) find that when bundling is allowed, there always exists an efficient equilibrium but inefficient equilibria can also exist due to pure bundling (for physical products) or slotting contracts. Under sequential pricing, we find that all equilibria are efficient regardless of whether firms can use slotting contracts, and both for digital goods and for physical goods. Therefore, sequential pricing presents an even stronger case for laissez-faire in the matter of bundling than simultaneous pricing.

This paper describes the impact of external environmental forces on cartel networks. Using a case research approach, this report examines two leading business networks within one industry, over time. The results suggest that (a) bargaining power of intermediaries increases with the advent of new and powerful actors, (b) process activities that cartels previously controlled are being outsourced to new actors sometimes based in developing countries, (c) other actors are acquiring resources once dominated by a cartel, (d) external forces triggered by the illegal diamond trade, such as international regulatory constraints, no longer favour cartels like De Beers, and (e) over time, these and additional environment factors are forcing actors like De Beers who perform rigid process activities to become more flexible. For example, forces are moving cartels which relied previously on hand-picked intermediaries in highly controlled networks to market their products to adopt a flexible market-focused expansion of operations in retail contexts.

Consideration was given to a model of the multilevel hierarchical structure whose elements strive to maximize the difference between the stimulation and the costs of managing the subordinated elements by reorganizing the inferior structural part. For different variants of information about the cost functional, solved was the problem of choosing the optimal stimulation that provides an equilibrium structure (where restructuring is not advantageous to the elements) with the minimum total payments.

Previous models of collective action assume that the network structure of individual relations that transmit social control mechanisms promoting or inhibiting collective action is given. An extended game-theoretical model that incorporates social control mechanisms as side payments and allows for endogenous network change is presented here. The model represents collective action as a public goods game and predicts that network clustering undermines mass public good production and the possibility of deleting ties leads towards equilibrium structures in which contributors and defectors are segregated. It is argued and elaborated how laboratory experiments with virtual social networks can be used to test these model predictions. An innovative experimental method is proposed, in which subjects are seated behind computers that are connected according to simple network structures. Subjects are informed about the decisions of their contacts and could send happy or sad smiley symbols to them, which are two possible operationalizations of social control mechanisms. In addition, subjects could delete existing links in reaction to collective action outcomes or to avoid unpleasant forms of social control. Results of a larger series of experimental tests are to follow.

We consider a network game where the nodes of the network wish to form a graph to route traffic between themselves. We present a model where costs are incurred for routing traffic, as well as for a lack of network connectivity. We focus on directed links and the link stability equilibrium concept, and characterize connected link stable equilibria. The structure of connected link stable networks is analyzed for several special cases.

We examine whether strong networks among incumbent venture capitalists (VCs) in local markets help restrict entry by outside VCs, thus improving incumbents' bargaining power over entrepreneurs. More densely networked markets experience less entry, with a one-standard deviation increase in network ties among incumbents reducing entry by approximately one-third. Entrants with established ties to target-market incumbents appear able to overcome this barrier to entry; in turn, incumbents react strategically to an increased threat of entry by freezing out any incumbents who facilitate entry into their market. Incumbents appear to benefit from reduced entry by paying lower prices for their deals. Copyright (c) 2010 The American Finance Association.

We study networks of relations – groups of agents linked by several cooperative relationships – exploring equilibrium conditions under different network configurations and information structures. Relationships are the links through which soft information can flow, and the value of a network lies in its ability to enforce agreements that could not be sustained without the information and sanctioning power provided by other network members. The model explains why network closure is important; why stable subnetworks may inhibit more valuable larger networks; and why information flows and action choices cannot be analyzed separately. Contagion strategies are suboptimal here, as they inhibit information transmission, delaying punishments.

Literature on network formation typically assumes that people create and remove relations as to maximize their outcome in the network. It is typically neglected that people might also care about the outcomes of others when creating and removing links. In the current paper, we set up an experiment in order to investigate whether people show preferences for the outcomes of others during network formation. We do not find strong evidence for such claims, and most of our data can be explained by assuming self-interest. Social motives only seem to play a role if a subject’s actions have a strong effect on the outcome of a specific other for which they have a reason to feel responsible. These findings suggest that in more complex settings, social motives play less of a role than in simple interaction situations.

Wir umreißen in dieser Arbeit die fachübergreifende Vielfalt an Netzwerkverbindungsspielen in der gegenwärtigen Forschung. Unser Fokus liegt auf einem Spiel, in dem egoistisch agierende Akteure untereinander Verbindungen und schließlich ein zusammenhängendes Netzwerk errichten. Wir fassen die Ergebnisse über Nash-Gleichgewichte in diesem Spiel und den dadurch implizierten Effizienzverlust von dezentralen Lösungen gegenüber einer zentralen Optimierung zusammen. Anschließend erweitern wir das Spiel derart, dass nun auch nicht-zusammenhängende Netzwerke entstehen können. Wir zeigen, unter welchen Bedingungen solche Netzwerke möglich sind und wie sie den maximalen Effizienzverlust, den sogenannten "Price of Anarchy", beeinflussen. We sketch the multidisciplinary diversity of network creation games in current research. There is a focus on a game where selfish player establish connections that entail a connected network. We summarize results on Nash Equilibria and the inefficiency of decentralized solutions in this game. Afterwards we introduce an extension of the game, that allows for disconnected networks. Conditions for the existence of disconnected Nash Equilibria and there effect on the price of anarchy are analyzed.

We present a model of endogenous network formation with absolute friction and heterogeneous agents. The individual payoffs from a given network are determined by the difference of an agent specific utility function that depends on the number of his/her direct links and the sum of his/her link-costs. These link-costs decompose in a symmetric function that represents the social and geographical distance between the two agents and an agent specific function representing the partner’s wealth and status. From a theoretical point of view, we define a new stability concept that is situated between the notions of pairwise stability (see Jackson and Wolinsky (1996)) and strong stability (see Dutta and Mutuswami (1997)). We show that our model has a unique stable network and we demonstrate that it is also strongly stable. As such, we provide uniqueness and existence for a whole range of stability concepts situated between our new stability concept and strong stability. From a practical point of view, we provide an algorithm that reproduces this stable network from information on the individual payoff structure. We illustrate the use of this algorithm by applying it to an informal insurance data set from the village of Nyakatoke in rural Tanzania.

We provide existence results in a game with local spillovers where the payoff function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks. Moreover, our existence proof allows us to characterize a pairwise equilibrium of these networks.

This paper considers the Bak—Sneppen (B&S) Self-Organized Criticality model originally developed for species co-evolution.
We focus both on the original application of the model on a lattice, and on scale-free networks. Stylized facts on firms size
distribution are also considered for the application of the model to the analysis of firms size dynamics. Thus, the B&S dynamics
under the uniform, Normal, lognormal, Pareto, and Weibull distributions is studied. The original model is also extended by
introducing weights on links connecting species, and examining the topology of the resulting Minimum Spanning Tree (MST) of
the underlying network. In a system of firms a MST may evidence the template of the strongest interactions among firms. Conditions
that lead to particular configurations of a MST are investigated.

In this paper we study the structure of the bilateral communication links within Online Consumer Communication Networks (OCCNs), such as virtual communities. Compared to the offline world, consumers in online networks are highly flexible to choose their communication partners and little is known about how this affects communication exchange structures. We analyze these structures by using a general approach from the game-theoretic literature of social and economic network formation where individuals trade off the cost of forming and maintaining links against the potential rewards of doing so, which results in a stable network structure. In our analysis, a combination of aspects common to OCCNs is incorporated that has not been investigated in this literature until now. First, the negative externality of communication specificity is included in the sense that the more direct connections an individual has to maintain with other individuals, the less she is able to specify her attention per link within her total time available. Therefore, the additive value per individual of her communications declines with an increasing number of links, and she also derives less additive value per individual from others with an increasing number of links. Second, a distinction is made between the social and informational value of communication, where informational communication value is assumed to be transferable via indirect links, whereas social communication value is not transferable. Analytical results are derived by using the concept of pairwise stability. A tendency towards fragmented pairwise stable structures - consisting of small, disjoint (star) components - is discovered, which can be attributed to the joint effect of the two aspects mentioned. We demonstrate that only some of the pairwise stable structures provide optimal welfare (total payoffs), and that the relative focus on informational versus social value of communication affects this welfare.

This paper presents an equilibrium theory of vertical mergers that incorporates strategic behaviors in the Hotelling-type location model. This enables one to consider the relationship between downstream firms' strategies for product differentiation and vertical integration. I show that vertical integration enhances the degree of product differentiation of the integrated firm. Under some conditions, partial integration arises in equilibrium, which may increase the profit of the nonintegrated downstream firm. The paper also discusses the welfare implications of vertical integration. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd. and the Editorial Board of The Journal of Industrial Economics.

This paper studies the effectiveness of two different antitrust policies by characterizing the network structure of market-sharing agreements that arises under those settings. Market-sharing agreements prevent firms from entering each other's market. The set of these agreements defines a collusive network, which is pursued by antitrust authorities. This article shows that under a constant probability of inspection and a penalty equal to a firm's limited liability, firms form collusive alliances where all of them are interconnected. In contrast, when the antitrust policy reacts to prices in both dimensions - probability of inspection and penalty - firms form collusive cartels where they are not necessarily fully interconnected. This implies that more competitive structures can be sustained in the second case than in the first case. Notwithstanding, antitrust laws may have a pro-competitive effect in both scenarios, as they give firms in large alliances more incentives to cut their agreements at once.

In this short introductory course to graph theory, possibly one of the most propulsive areas of contemporary mathematics,
some of the basic graph-theoretic concepts together with some open problems in this scientific field are presented.

There has been recent interest in showing that real networks, designed via optimization, may possess topological properties similar to those investigated by the Network Science community. This suggests that the Network Science community's view that topological properties such as scale-freeness are not the result of some immutable physical laws, but in fact intentional optimization. Recently, it was shown that stable graphs with an arbitrary degree sequence may result from a stability point of a collaborative game. In this paper, we present an integer program (IP) whose solutions yield graphs with a degree sequence, that is closest to a given degree sequence in the Manhattan metric. Stable graphs to the graph formation game and solutions to the IP in this paper, may be non-unique. We relate graphical solutions of the given IP to stable collaboration networks via the price of anarchy which we can calculate exactly as the result of another integer program.

We extend the differentiated product model, first developed by Bowley (1924), by relaxing the assumption that each firm produces only one differentiated product. By doing so, we are able to analyze the potential for collusive market segmentation in a two stage decision framework, first in product space and second in output. We find that when firms cannot coordinate on output, the required discount factor that supports collusive market segmentation is strictly decreasing in product substitutability and is greater than partial output and full collusion. Overall we find that output collusion alone is easier to sustain than collusive product market segmentation.

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.

This paper introduces a certain graphical coalitional game where the internal topology of the coalition depends on a prescribed communication graph structure among the agents. The game Value Function is required to satisfy four Axioms of Value. These axioms make it possible to provide a refined study of coalition structures on graphs by defining a formal graphical game and by assigning a Positional Advantage, based on the Shapley value, to each agent in a coalition based on its connectivity properties within the graph. Using the Axioms of Value the graphical coalitional game can be shown to satisfy properties such as convexity, fairness, cohesiveness, and full cooperativeness. Three measures of the contributions of agents to a coalition are introduced: marginal contribution, competitive contribution, and altruistic contribution. The mathematical framework given here is used to establish results regarding the dependence of these three types of contributions on the graph topology, and changes in these contributions due to changes in graph topology. Based on these different contributions, three online sequential decision games are defined on top of the graphical coalitional game, and the stable graphs under each of these sequential decision games are studied. It is shown that the stable graphs under the objective of maximizing the marginal contribution are any connected graph. The stable graphs under the objective of maximizing the competitive contribution are the complete graph. The stable graphs under the objective of maximizing the altruistic contribution are any tree.

Harrington et al. (Math Program Ser B 104:407–435, 2005) introduced a general framework for modeling tacit collusion in which producing firms collectively maximize the Nash bargaining objective function, subject to incentive compatibility constraints. This work extends that collusion model to the setting of a competitive pool-based electricity market operated by an independent system operator. The extension has two features. First, the locationally distinct markets in which firms compete are connected by transmission lines. Capacity limits of the transmission lines, together with the laws of physics that guide the flow of electricity, may alter firms’ strategic behavior. Second, in addition to electricity power producers, other market participants, including system operators and power marketers, play important roles in a competitive electricity market. The new players are included in the model in order to better represent real-world markets, and this inclusion will impact power producers’ strategic behavior as well. The resulting model is a mathematical program with equilibrium constraints (MPEC). Properties of the specific MPEC are discussed and numerical examples illustrating the impacts of transmission congestion in a collusive game are presented.

Many financial markets are characterized by strong relationships and networks, rather than arm's-length, spot-market transactions. We examine the entry-deterring effects of this organizational choice in the context of relationships established when VCs syndicate portfolio company investments using U.S. data for the period 1980 to 2003. Our results show that networking does present an effective barrier to entry: VC markets with more extensive networking among the incumbent players experience less entry, and the economic effect is sizeable. However, potential entrants can use their prior relationships with the incumbents as well as previous investment experience in the industry or state to overcome this barrier to entry. We also document that companies seeking venture capital are valued less highly in better protected markets, and that increased entry into a market is associated with companies receiving increased valuations.

This work is a review of previous works on the stopping laws in networks. Among other results, we show a non combinatorial
method to compute the stopping law, the existence of a minimal Markov chain without oversized information, the existence of
a polynomial algorithm which projects the Markov chain onto the minimal Markov chain. Several applied examples are presented.

This paper presents an equilibrium theory of vertical mergers that incorporates strategic behaviors in the Hotelling-type location model. This enables one to consider the relationship between downstream firms' strategies for product differentiation and vertical integration. I show that vertical integration enhances the degree of product differentiation of the integrated firm. Under some conditions, partial integration arises in equilibrium, which may increase the profit of the nonintegrated downstream firm. The paper also discusses the welfare implications of vertical integration.

We model strategic communication network formation with (i) link specificity: link maintenance lowers specific attention and thus value (negative externality previously ignored for communication) and (ii) value transferability via indirect links for informational but not for social value (positive externality modeled uniformly before). Assuming only social value, the pairwise stable set includes many nonstandard networks under high and particular combinations of complete components under low link specificity. Allowing for social and informational value reduces this set to certain fragmented networks under high and the complete network under low link specificity. These extremes are efficient, whereas intermediate link specificity generates inefficiency.

Purpose – This paper aims to explore the three basic roles that access price plays: the collection of opportunity cost; the redistribution of profit; and the tools of exploiting competitors. Design/methodology/approach – The paper uses the efficient component pricing rule. Findings – According to the model constructed in this paper, it is found that, unless the basic commodities are the substitutes (independent) for combined goods, the opportunity cost arising from the access process is not necessarily positive. Besides, this analysis reveals that among the combined access prices there exist certain crowding-out effects. Social implications – This paper finds that the access commodities' collusion equilibrium does not exist. Originality/value – This paper adopts a more generalized set-up to analyze the problem of access pricing. Besides, since the collection of opportunity cost is the most common and reasonable explanation for the existence of access pricing, this study conducts further analysis on this topic.

We model the formation of networks as a game where players aspire to maximize
their own centrality by increasing the number of other players to which they
are path-wise connected, while simultaneously incurring a cost for each added
adjacent edge. We simulate the interactions between players using an algorithm
that factors in rational strategic behavior based on a common objective
function. The resulting networks exhibit pairwise stability, from which we
derive necessary stable conditions for specific graph topologies. We then
expand the model to simulate non-trivial games with large numbers of players.
We show that using conditions necessary for the stability of star topologies we
can induce the formation of hub players that positively impact the total
welfare of the network.

This paper presents some recent developments in the theory of coalition and network formation. For this purpose, a few major equilibrium concepts recently introduced to model the formation of coalition structures and networks among players are briey reviewed and discussed. Some economic applications are also illustrated to give a avour of the type of predictions such models are able to provide.

The purpose of the paper is to provide a simple model explaining buyer-supplier relationships and show what factors determine the number of trading partners. We show that when the supplier is able to determine the number of trading partners, the optimal number is small if the supplier's bargaining power with them is weak, the economy of scope in the supplier's variable costs is significant, and that in its sunk investment is weak. Investment may be greater when the number of trading partners is small. The results may be consistent with the formation of Japanese buyer-supplier relations.

Since the seminal contribution of Jackson & Wolinsky 1996 [A Strategic Model of Social and Economic Networks, JET 71, 44-74] 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 gap by analyzing the role of positive and negative externalities of link formation. We find general results that relate situations of positive externalities with stable networks that cannot be "too dense" in a well-defined sense, while situations with negative externalities, tend to induce "too dense" networks.

This paper investigates the strategic formation of collusive networks in a dynamic framework. A collusive network is a set
of market sharing agreements between firms in oligopolistic markets and auctions. Belleflamme and Bloch (Int Econ Rev 45(2):387–411,
2004) fully characterize the pairwise stable collusive networks in their symmetric model. In contrast, we characterize the
collusive networks to which a dynamic network formation process converges with positive probability in the symmetric model.
We provide a complete characterization for the case of the process that starts from a network with sufficiently few links.
Moreover, we show that the process never cycles but always converges to a stable network. In addition, we discuss an asymmetric
model where firms enjoy a home country advantage. We show that the expected number of collusive agreements may be reduced
by an increase in the degree of the home country advantage. This implies that policies for discouraging entry may fail, and
may lead to a decrease in expected social surplus.

Empirical work suggests that social and economic networks are characterized by an unequal distribution of connections across individuals. This paper explores the circumstances under which networks will or will not exhibit inequality. Two specific models of network formation are explored. The first is a playing the field game in which the aggregate payoffs of an individual depend only on the number of his links and the aggregate number of links of the rest of the population. The second is a local spillovers game in which the aggregate payoffs of an individual depend on the distribution of links of all players and the identity of neighbors. For both class of games we develop results on existence and characterize equilibrium networks under different combinations of externalities/spillovers. We also examine conditions under which having more connections implies a higher payoff.

[fre] Cet article présente un panorama de recherches récentes sur la formation de réseaux inter-firmes. Ces réseaux sont considérés dans deux types d'environnement économique. Nous étudions tout d'abord des réseaux de collaboration horizontale entre firmes. Puis nous analysons des réseaux de relations verticales (telles que client/fournisseur). Nous examinons les architectures de réseaux stratégiquement stables et la relation entre incitation individuelle et surplus social dans les réseaux. [eng] This paper presents a survey of recent research on the formation of networks between firms. The paper considers networks in two economic environments. We first consider networks of research collaboration between horizontally related firms. We then study networks between vertically related firms (such as buyers and sellers). We examine the architecture of strategically stable networks and the relation between individual incentives and social welfare in networks.

In this article we investigate the incentive to merge when firms that produce differentiated products engage in price competition. We demonstrate that mergers of any size are beneficial and are so increasingly: large mergers yield higher profits than smaller ones. This is in contrast to the result that mergers tend to be disadvantageous in quantity-setting games. This qualitative difference follows from the fact that reaction functions are typically upward sloping in price games but downward sloping in quantity games. Thus, the reaction of outsiders reinforces the initial price increase that results from the merger.

In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per firm output.) In both cases, per-firm profits are decreasing. The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into the existence of Cournot equilibrium is developed.

In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per firm output.) In both cases, per-firm profits are decreasing. The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into the existence of Cournot equilibrium is developed. Copyright 2000 by The Review of Economic Studies Limited

Preface. Part I: Social and Economic Networks in Cooperative Situations. 1. Games and Networks. 2. Restricted Cooperation in Games. 3. Inheritance of Properties in Communication Situations. 4. Variants on the Basic Model. Part II: Network Formation. 5. Noncooperative Games. 6. A Network-Formation Model in Extensive Form. 7. A Network-Formation Model in Strategic Form. 8. Network Formation with Costs for Establishing Links. 9. A One-Stage Model of Network Formation and Payoff Division. 10. Network Formation and Potential Games. 11. Network Formation and Reward Functions. References. Notations. Index.

Inequalities. By Hardy G.H. , Littlewood J.E. and Pólya G. . 2nd edition. Pp. xii, 324. 27s. 6d. 1952. (Cambridge University Press) - Volume 37 Issue 321

The gains from cartel formation and the stability of a dominant cartel are investigated for the price-leadership model. We show that there is a general interest in the establishment of a cartel with the competitive fringe reaping a disproportionate share of the benefits. In contrast to results involving a continuum of firms, with a finite number of firms (each with the same cost curve) there is always a stable dominant cartel. /// A propos de la stabilité d'une structure de marché caractérisée par la collusion de firmes dominantes pour établir un leadership de prix. Le mémoire étudie les gains dérivés de la formation d'un cartel et la stabilité d'un cartel dominant dans le cadre d'un modèle de leadership de prix de la firme dominante. On montre qu'il y a un intérêt général à créer un cartel même si les firmes satellites à la périphérie du cartel ramassent une part plus que proportionnelle des bénéfices. Contrairement à ce que l'on observe quand on est en présence d'un continuum de firmes, quand leur nombre est fini -- chacune avec la même courbe de coûts -- il y a toujours un cartel dominant stable.

This paper argues that the sign of external effects of coalition formation provides a useful organizing principle in examining economic coalitions. In many interesting economic games, coalition formation creates eithernegativeexternalities orpositiveexternalities for nonmembers. Examples of negative externalities are research coalitions and customs unions. Examples of positive externalities include output cartels and public goods coalitions. I characterize and compare stable coalition structures under the following three rules of coalition formation: the Open Membership game of Yi and Shin (1995), the Coalition Unanimity game of Bloch (1996), and the Equilibrium Binding Agreements of Ray and Vohra (1994).Journal of Economic LiteratureClassification Numbers: C72, C71.

The theory presented in this paper investigates the connection between the number of competitors and the tendency to cooperate within the context of a symmetric Cournot model with linear cost and demand, supplemented by specific institutional assumptions about the possibilities of cooperation. Cooperative forms of behavior are modelled as moves in a non-cooperative game. The proposition that few suppliers will maximize their joint profits whereas many suppliers are likely to behave non-cooperatively does not appear as an assumption but as a conclusion of the theory. For the simple model analyzed in this paper a definite answer can be given to the question where a small group of competitors ends and a large group begins: 5 is the dividing line between few and many.

In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost
functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing
industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per firm output.)
In both cases, per-firm profits are decreasing.
The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions
of a global nature. As a byproduct of independent interest, new insight into the existence of Cournot equilibrium is developed.

We study the stability and efficiency of social and economic networks, when self-interested individuals have the discretion to form or sever links. First, in the context of two stylized models, we characterize the sets of stable networkds (immune to incentives to form or sever links) and the sets of efficient networks (those which maximize total production or utility). The sets of stable networks and efficients networks do not always intersect. Next, we show that this tension is not unique to these models, but persists generally. In order to assure that there is always at least one efficient graph which is stable, one is forced to allocate resources to nodes (players) who are not responsible for any of the production. We characterize one such allocations rule: the equal split rule. We characterize another rule which fails to assure that efficient graphs are stable, but arises naturally if the allocations result from the bargaining of players.

Extending the Revelation Principlé to a case in which it is costly for the principal to communicate with any agent, we show that there is a sequential direct mechanism that is optimal in the class of all mechanisms. We then apply this result to the problem of a monopsonist seeking to buy an indivisible good from one of a set of possible sellers with unobservable production costs. With costly communication, the monopsonist's optimal procurement mechanism is a combination of reservation-price search and auction.

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say [alpha], is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good [alpha] are higher when good [alpha] is sold first.

The existence of a negative relationship between cartel stability and the level of excess capacity in an industry has for a long time been the dominant view in the traditional IO literature. Recent supergame-theoretic contributions (e.g. Brock and Scheinkman, 1985) appear to show that this view is ill-founded. Focussing on the issue of enforcement of cartel rules ('incentive contraints'), however, this literature completely ignores firms' 'participation constraints'. Reverting the focus of attention, the present paper restores the traditional view: large cartels will not be sustainable in periods of high excess capacity (low demand). In contrast to the supergame-theoretic literature, it predicts a negative relationship between excess capacity and the collusive price.

This paper examines the bidding for school milk contracts in Florida and Texas during the 1980s. In both states firms were
convicted of bid-rigging. The data and legal evidence suggest that the cartels in the two states allocate contracts in different
ways: One cartel divides the market among members, while the other cartel also uses side payments to compensate members for
refraining from bidding. We show that both forms of cartel agreements are almost optimal, provided the number of contracts
is sufficiently large.
In the auction the cartel bidder may face competition from non-cartel bidders. The presence of an optimal cartel induces an
asymmetry in the auction. The selected cartel bidder is bidding as a representative of a group and has on average a lower
cost than a non-cartel bidder. The data support the predicted equilibrium bidding behaviour in asymmetric auctions in accordance
with optimal cartels.

We present an approach to network formation based on the notion that social networks are formed by individual decisions that trade off the costs of forming and maintaining links against the potential rewards from doing so. We suppose that a link with another agent allows access, in part and in due course, to the benefits available to the latter via his own links. Thus individual links generate externalities whose value depends on the level of decay/delay associated with indirect links. A distinctive aspect of our approach is that the costs of link formation are incurred only by the person who initiates the link. This allows us to formulate the network formation process as a noncooperative game.
We first provide a characterization of the architecture of equilibrium networks. We then study the dynamics of network formation. We find that individual efforts to access benefits offered by others lead, rapidly, to the emergence of an equilibrium social network, under a variety of circumstances. The limiting networks have simple architectures, e.g., the wheel, the star, or generalizations of these networks. In many cases, such networks are also socially efficient.

This discussion paper has resulted in a publication in the Rand Journal of Economics , 2001, 32(4), 686-707.

We study the incentives for a "diagonal" merger between two Internet Service Providers, one a wireless retail only ISP in two origination markets, and the second a vertically integrated wired retailer in one market and an upstream provider in the other. The merger's effects depend on differentiation in access modalities; only with high differentiation does the merger have positive welfare effects. We focus on post-merger foreclosure, which, when it happens, only takes place in the market where the merger is horizontal and not where the merger is vertical. The Network architecture used is meant to capture Internet routing.

In recent years, there has been a great deal of research on the relative merits of multilateralism and bilateralism and their implications for the nature of the trading regime between countries. In this paper we explore the scope of bilateral free-trade agreements as a foundation for free trade, using recent developments in the theory of strategic network formation. We study a setting with many contries; in each country there are firms, which can sell in the domestic market as well as sell in the foreign markets. The possibility of selling in foreign markets depends on the nature of import tariffs faced by firms. Countries can sign bilateral free-trade agreements which lower import tariffs and thereby facilitate trade. We allow a country to sign any number of bilateral trade agreements. A profile of trade agreements defines the trading regime. We study the nature of trading regimes that are consistent with the incentives of individual countries. Our principal finding is that bilateralism is consistent with global free trade.

The authors characterize coordinated bidding strategies in two cases: a weak cartel, in which the bidders cannot make side-payments; and a strong cartel, in which the cartel members can exclude new entrants and can make transfer payments. The weak cartel can do no better than have its members submit identical bids. The strong cartel in effect reauctions the good among the cartel members. Copyright 1992 by American Economic Association.

- And J L Moraga
- Hardy Networks
- J E Littlewood
- And G P Olya

——, AND J. L. MORAGA, " R&D Networks, " Rand Journal of Economics 32 (2001), 686–707.
HARDY, G. H., J. E. LITTLEWOOD, AND G. P ´
OLYA, Inequalities (Cambridge: Cambridge University Press, 1952).

Common Carrier Bureau Tentatively Agrees on Conditions for SBC-Ameritech Merger

- And Pickering

WILMER, CUTLER, AND PICKERING, " Common Carrier Bureau Tentatively Agrees on Conditions for SBC-Ameritech Merger, " Telecommunications Law Updates (July 1999).

- Game Theory

MYERSON, R. B., Game Theory: Analysis of Conflict (Cambridge, MA: Harvard University
Press, 1991).

Cartel Watch Competition Authority Guidelines on Cartels: Detection and Remedies Available at www.irlgov.ie A Strategic Model of Social and Economic Networks

- Irish Competition Authorityhtm
- And A Wolinsky

IRISH COMPETITION AUTHORITY, " Cartel Watch. Competition Authority Guidelines on
Cartels: Detection and Remedies, " 1999. Available at www.irlgov.ie/compauth/
CARTEL.htm
JACKSON, M. O., AND A. WOLINSKY, " A Strategic Model of Social and Economic Networks, "
Journal of Economic Theory 71 (1996), 44–74.

- L Lovasz