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Abstract

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