Network potentials

A network payoff function assigns a utility to all participants within a social network. In this paper we investigate network payoff functions that admit an exact network potential or an ordinal network potential. We also investigate exact and ordinal potentials of Myerson’s non-cooperative network formation game based on consent in link formation. We show that the admittance of certain of these network and game-theoretic potentials implies the existence of pairwise stable networks and the convergence of network formation processes. Our main results extend and strengthen the current insights in the literature on game theoretic approaches to social network formation. We thank Matt Jackson and Sudipta Sarangi for extensive discussions on the subject of this paper. Part of this research was done while S. Chakrabarti was at Bonn on a post-doctoral research fellowship. We thank the Department of Economics at the University of Bonn for their hospitality and financial support. Part of this research was done at the Center for Economic Research at Tilburg University, Tilburg, the Netherlands. R. P. Gilles financially supported from the Netherlands Organization for Scientific Research (NWO), grant # 46-550, is gratefully acknowledged.     

Stable and efficient bargaining networks

Abstract. We examine a bargaining game among players connected by a network, where successively potential partners negotiate over terms of a project. For any network structure and ordering of selection of bargaining partners, there is a unique subgame perfect equilibrium outcome which coincides with the standard Rubinstein split. Based on this, we derive expected payoffs for players as a function of the network. We the characterize the pairwise stable and efficient bargaining networks. These two sets do not always coincide and in many situations pairwise stable networks are over-connected. Received: 10 April 2001 / Accepted: 17 January 2002 I am indebted to Matthew Jackson for suggesting this paper. I also thank Bernard Caillaud, Sanjeev Goyal, and the seminar participants at Universidad de Alicante, Universidad Carlos III de Madrid, CEMFI (Madrid), Universitat Autònoma de Barcelona, Erasmus University of Rotterdam, Universitat Pompeu Fabra (Barcelona) and CERAS (Paris) for helpful comments. This paper was written while at Universitat Pompeu Fabra and CERAS. Financial support from the Spanish Ministry of Education through research grant DGESIC PB96-0302, and from the Ecole Nationale des Ponts et Chaussées, Paris is gratefully acknowledged. All errors are of course mine.     

A dynamic analysis of collusive 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.     

Strategy-proof allocation of fixed costs

An economy can produce and consume a fixed-cost excludable public good only if its members fully fund the cost of the good. In this paper, we characterize the entire class of mechanisms for the provision of the public good and its cost that are Pareto optimal among the set of strategy-proof, voluntarily-participatory, budget-balancing, non-bossy, and replacement-monotonic mechanisms. We demonstrate that this class of mechanisms is quite small and can be characterized as simple step-price mechanisms.Received: 10 July 2001, Accepted: 5 February 2003, JEL Classification: C72, D71This work was done while Dearden was visiting Center for Economic Research, Tilburg University, The Netherlands. He is thankful for their gracious hospitality. The authors thank the editors and reviewers for their thoughtful comments.     

Optimal design of trade institutions

We model an economy with social institutions that facilitate trade and induce three types of costs: establishment costs, access costs, and use costs. Use costs are specific transaction costs related to the use of these trade institutions. We assume that a trade institution is economically completely determined by the costs it imposes and by the effects on the trades it facilitates. We extend the Pareto efficiency concept to include various modes of organization of social institutions: the costs and benefits of these organizations are expressed in the trades they facilitate.Within this setting we discuss a valuation equilibrium concept, in which all agents use a common conjectural price system that assigns to every trade institution the price vector that would prevail under it. This feature of the equilibrium is important in securing the second welfare theorem, and is new to the analysis of economies with costly trade. Since the use costs can be nonlinear, there are non-convexities that prevent the second welfare theorem from obtaining in a finite economy, but we show it for large economies.Received: 3 April 2002, Accepted: 30 April 2003, JEL Classification: D59, D70, H49Robert P. Gilles: donewhile visiting the Center for Economic Research, Tilburg University, Tilburg, The Netherlands. Financial support from the Netherlands Organization for Scientific Research (NWO), grant B46-390, is gratefully acknowledged.Dimitrios Diamantaras: Part of this research wasSupport from Temple University via a Fuller research fellowship is gratefully acknowledged.The authors would like to thank Suzanne Scotchmer, Andreu Mas-Colell, Marcus Berliant, Shlomo Weber, Hans Haller, Dhanajay Gokhale, Julian Manning, and two anonymous referees for their valuable comments and discussions of previous drafts of this paper. A previous version of this paper was circulated as Equilibria of economies with costly trade.     

FROM EXOGENOUS TO ENDOGENOUS ECONOMIC NETWORKS: INTERNET APPLICATIONS

Abstract.  Economic agents' behaviour is affected by their position in a network, either exogenous or endogenous, in which they interact with a sub-set of neighbours only. The network's links, which may be generated by vertical and/or horizontal relations, or by more complex morphologies, may explain the transition between dynamic equilibria and the instability of economic aggregates. Moreover, networks shape strategic interaction among agents by determining their strategies; the problem of access and interconnection, particularly relevant in the Internet, is perhaps the best example. A two-way feedback between strategies and network structures arises instead when links are endogenous: those features are clearly shown in the mechanism underlying the formation of peering links and R & D networks.     

Under-connected and over-connected networks: the role of externalities in strategic network formation

Since the seminal contribution of Jackson and Wolinsky (J Econ Theory 71(1):44–74, 1996) 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. Those results are neither restricted to specific assumptions on the agents’ preferences (e.g. homogeneity), nor to a specific notion of stability or efficiency.     

Mediation and the Nash bargaining solution

This paper analyzes a model of bargaining in which two parties use a mediator who sequentially makes random proposals until agreement by both parties is reached. I show that as the cost of delay shrinks to zero, the subgame perfect payoff converges to the asymmetric Nash bargaining solution with weights determined by the relative discount rates of the players. I also establish conditions for the uniqueness of the subgame perfect equilibrium for arbitrary discount rates.     

When does universal peace prevail? Secession and group formation in conflict

This paper analyzes secession and group formation in the general model of contests due to Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a contest among singletons. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests. Received: March 2004, Accepted: October 2004, JEL Classification: D72, D74 We thank Joan Maria Esteban, Kai Konrad, Debraj Ray, Stergios Skaperdas and two anonymous referees for helpful comments on the paper. We also benefitted from comments by seminar participants in Barcelona, Istanbul, Paris and WZB Berlin.     

The evolution of free trade networks

This paper considers the evolutionary dynamics of a free trade agreement (FTA) network formation game among N countries. We first explore the static model introduced by Goyal and Joshi (2006) and precisely characterize the set of pairwise stable FTA networks. Then, we develop a dynamic model under random perturbations and identify long-run outcomes to remove prediction uncertainty inherited from static analysis. The results show that both partial free trade and global free trade will result when there are only three countries. However, when more countries are involved, only the complete FTA network emerges.     

Simple collective equilibria in stopping games

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.     

How to get firms to invest: A simple solution to the hold-up problem in regulation

Abstract. Many governmental programs are effective only if firms make costly investments. The inability of authorities to precommit to a regulatory scheme creates incentives for firms not to invest and to hold-up the regulator. This paper describes a simple subsidy/tax scheme embedded in a four-stage mechanism that solves the hold-up problem. We design a self-financing subsidy/tax scheme which benefits a complying firm at the expense of a non-complying firm. In order to be credible, the subsidy and tax rates must maximize social welfare for any combination of investment decisions. We show that there exists a unique subgame perfect equilibrium in which all firms invest and no actual implementation with subsidies and taxes is required. We discuss in which cases the mechanism can work under incomplete information. Received: 30 December 1998 / Accepted: 12 October 2001     

Coalition-proof stable networks

Review of Economic Design - We propose the notion of coalition-proof stability for predicting the networks that could emerge when group deviations are allowed. A network is coalition-proof stable...     

A strategic analysis of network reliability

Abstract. We consider a non-cooperative model of information networks where communication is costly and not fully reliable. We examine the nature of Nash networks and efficient networks. We find that if the society is large, and link formation costs are moderate, Nash networks as well as efficient networks will be ‘super-connected’ i.e. every link is redundant in the sense that the network remains connected even after the link is deleted. This contrasts with the properties of a deterministic model of information decay, where Nash networks typically involve unique paths between agents. We also find that if costs are very low or very high, or if links are highly reliable then there is virtually no conflict between efficiency and stability. However, for intermediate values of costs and link reliability, Nash networks may be underconnected relative to the social optimum.     

Private and Social Incentives for Vertical Contract Disclosure

We follow the framework in Arya and Mittendorf's 2011 Rand Journal of Economics paper but extend their analysis by investigating supplier(s)' equilibrium choices of disclosure or confidentiality regarding their contract terms with the downstream retailers. In the case of a common supplier, we find that the unique subgame perfect Nash equilibrium (SPNE) is for the supplier to choose disclosure. This private incentive is opposite to social incentive, which calls for the regulator to choose confidentiality. In the case of dedicated suppliers, however, there are multiple SPNE due to coordination issues between the suppliers. The case which maximizes social surplus – disclosure – can be supported as a SPNE, together with the case of confidentiality, which maximizes supplier profits at the cost of everyone else. Copyright © 2014 John Wiley & Sons, Ltd.     

Buyer–seller networks with demand shocks and intermediation

We present a model in which buyers and sellers use links to trade with each other. Each seller produces a good which can be one of two types. Buyers are ex ante identical but receive specification or valuation shocks after the links are formed. We show that efficient networks are stable and that severing a link in an efficient network results in a higher price for the buyer but a lower price for the seller. We also examine network intermediation when sellers (buyers) form links sequentially. When sellers form links sequentially, the first seller becomes an intermediary and shares links with other sellers; this makes all sellers better off. However, when buyers form links sequentially, buyers may or may not share links. If links are shared multiple intermediaries result.     

Trade through endogenous intermediaries

We propose an intermediation core for an economy that explicitly specifies how traders organize themselves into trade cooperatives (intermediaries) and how trade between them gets carried out. The intermediation core allocations are closely related to the equilibrium allocations of a non-cooperative intermediation game in Townsend (1983). We show that the intermediation core contains all subgame perfect equilibrium allocations of the intermediation game, similar to the inclusion of competitive equilibrium allocations in the core usually studied. We identify intermediation core allocations that are also subgame perfect equilibrium allocations of the intermediation game in terms of the supporting intermediary structures. These results help to characterize subgame perfect equilibrium allocations of the intermediation game and to analyze their welfare and stability properties.     

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game G^S,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game.By a modification of G^S,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.     

The stability and efficiency of directed communication networks

Abstract. This paper analyzes the formation of directed networks where self-interested individuals choose with whom they communicate. The focus of the paper is on whether the incentives of individuals to add or sever links will lead them to form networks that are efficient from a societal viewpoint. It is shown that for some contexts, to reconcile efficiency with individual incentives, benefits must either be redistributed in ways depending on “outsiders” who do not contribute to the productive value of the network, or in ways that violate equity (i.e., anonymity). It is also shown that there are interesting contexts for which it is possible to ensure that efficient networks are individually stable via (re)distributions that are balanced across components of the network, anonymous, and independent of the connections of non-contributing outsiders.     

Hotelling was Right

This paper proves existence of a subgame perfect equilibrium in Hotelling's original (unidimensional city, linear transportation costs, uniform distribution of the consumers, two firms with identical and constant marginal cost, perfectly inelastic demand) location–price game such that in the location subgame the location choices of the firms are pure and identical. The result can be extended to variations of the original setup (multidimensional city, nonlinear transportation costs, nonuniform distribution of consumers, many firms with identical and constant marginal costs, two or more firms with nonidentical but constant marginal costs).