Stochastic stability in networks with decay

This paper considers a stylized model of network formation in which relations among agents are subject to frictions, as described in Bala and Goyal [A non cooperative model of network formation, Econometrica 68 (2000) 1181-1231]. We analyze the process of network formation in a dynamic framework where self-interested individuals can form or delete links and, occasionally, make mistakes. Then, using stochastic stability, we identify the network structures to which the formation process will converge.     

Farsighted network formation

This paper studies a model of dynamic network formation when individuals are farsighted: players evaluate the desirability of a “current” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account farsighted behavior of agents and allows for limited cooperation amongst agents. We show that an equilibrium process of network formation exists. We also show that there are valuation structures in which no equilibrium strategy profile can sustain efficient networks. We then provide sufficient conditions under which the equilibrium process will yield efficient outcomes.     

Redistributive taxation in a simple perfect foresight model

We investigate the redistributive potential of capital taxation in an intertemporal maximizing model of capital formation. First, even unanticipated redistributive capital taxation is severely limited in its effectiveness since it depresses wages. Second, under any convergent redistributive tax policy which maximizes a Paretian social objective, the capital income tax will converge to zero, independent of the factor supply elasticities. These results are independent of workers' holdings of capital.     

Dynamics in tree formation games

Network formation games capture two conflicting objectives of selfish nodes in a network: such nodes wish to form a well-connected network and, at the same time, to minimize their cost of participation. We consider three families of such models where nodes avoid forming edges beyond those necessary for connectivity, thus forming tree networks. We focus on two local two-stage best-response dynamics in these models, where nodes can only form links with others in a restricted neighborhood. Despite this locality, both our dynamics converge to efficient outcomes in two of the considered families of models. In the third family of models, both our dynamics guarantee at most constant efficiency loss. This is in contrast with the standard best-response dynamics whose efficiency loss is unbounded in all three families of models. Thus we present a globally constrained network formation game where local dynamics naturally select desirable outcomes.     

Better-reply dynamics and global convergence to Nash equilibrium in aggregative games

We consider n-person games with quasi-concave payoffs that depend on a player's own action and the sum of all players' actions. We show that a discrete-time, stochastic process in which players move towards better replies—the better-reply dynamics—converges globally to a Nash equilibrium if actions are either strategic substitutes or strategic complements for all players around each Nash equilibrium that is asymptotically stable under a deterministic, adjusted best-reply dynamics. We present an example of a 2-person game with a unique equilibrium where the derivatives of the best-reply functions have different signs and the better-reply dynamics does not converge.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Competition and open source with perfect software compatibility

In this paper we study duopolistic competition between closed and open source software. Inspired by recent contributions on open source, we propose a two-stage game with perfect information and product differentiation, in which producers first set software quality and then determine prices (the price is zero for open source programs). We assume perfect software compatibility and model lock-in effects, a network externality component of software quality, and accumulation of experience in software use and implementation. In comparison to the monopolistic benchmark case, we argue that, in a duopoly created by the emergence of an open source program, the proprietary software producer will reduce its selling price if: (i) its network of users is larger than the open source network and its consumers are largely familiar with its program, (ii) it has a small network of unskilled consumers. On the other hand, the price of proprietary software will increase if its users form a large, but poorly-skilled network. Furthermore, we show that, in all of the above cases, the hedonic quality of proprietary software increases. Finally, by modeling experience accumulation processes through difference equations, we show that the ratio between the closed and open source programs’ opportunity costs for software learning and deployment plays a crucial role in shaping market outcomes. If open source software remains too complex and technical for unskilled or time-pressed users, a shared market solution, in which both programs are adopted, is likely to emerge. However, if opportunity costs in learning and understanding open source programs are particularly low, or at least equal to the opportunity costs of a closed-source program, then open source dominance emerges (i.e. markets tip to open source).     

Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox

The Braess Paradox consists of showing that, in equilibrium, adding a new link that connects two routes running between a common origin and common destination may raise the travel cost for each network user. We report the results of two experiments designed to study whether the paradox is behaviorally realized in two simulated traffic networks that differ from each other in their topology. Both experiments include relatively large groups of participants who independently and repeatedly choose travel routes in one of two types of traffic networks, one with the added links and the other without them. Our results reject the hypothesis that the paradox is of marginal value and its force diminishes with experience. Rather, they strongly support the alternative hypothesis that with experience in traversing the networks financially motivated players converge to choosing the equilibrium routes in the network with added capacity despite sustaining a sharp decline in earnings.     

Networks of Free Trade Agreements among Heterogeneous Countries

The paper examines the formation of free trade agreements as a network formation game. We consider an n‐country model in which international trade occurs between economies with imperfectly competitive product markets. In each country, the labor market is either unionized or non‐unionized. We show that, if all countries are non‐unionized, the global free trade network is both the unique pairwise stable network and the unique efficient network. If all countries are unionized, the global free trade network is pairwise stable and the unique efficient network among the class of symmetric networks. If some countries are unionized while others are non‐unionized, other networks apart from the global free trade network may be pairwise stable. However, the efficient network is still the global free trade network. Thus, a conflict between stability and efficiency may occur. Moreover, starting from the network in which no country has signed a free trade agreement, all sequences of networks due to continuously profitable deviations do not lead (in most cases) to the global free trade network, even when global free trade is stable.     

The Evolution of Social and Economic Networks

We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead to any given network at some time, where the stochastic process selects from among the statically stable networks and cycles. We apply these results to examples including the Gale-Shapley marriage problem. Thus the paper achieves two goals. First, it outlines a dynamic solution concept for networks. Second, it applies this concept to matching problems. Journal of Economic Literature Classification Numbers: A14, D20, J00.     

基于城市空间结构和交通区位分析的轨道交通线网布局方法研究

城市轨道交通线网的布局合理与否,将直接影响未来城市的发展和空间结构的形成.应用交通区位理论,将“点、线、面”三要素层次分析法与之相结合,并进行控制点优化,从而提出一种基于城市空间结构及交通区位分析的线网布局方法,并以哈尔滨市为实例分析,将此方法应用于目前轨道网的调整规划之中,得到较为合理的轨道交通线网布局规划方案.     

Policy issues in the development of telecommunications

The paper examines the specific features of the telecommunications system which determine its character, and the regulatory issues which arise out of a situation of potential conflict between the telecommunications network operators (PITs) and the providers and consumers of value added services transacted on the network. It looks at the policy options available to reconcile such conflicts, and at how EC policies are shaping the future of the European telecommunications ststem. It concludes that current development in telematics are aimed mainly at business users, and that safeguards for the private custormer will be necessary in order to ensure the provision of a socially equitable service.     

A heuristic procedure to identify the most valuable chain of patent priority network

In this study, we provide support for the argument that patents are at their maximum value at those times when they are under litigation. We develop a heuristic procedure to determine the way in which such patents under litigation form a network of patent family members, and then go on to examine the priority patents involved. We subsequently attempt to develop a simple procedure to further identify both the ‘critical’ and ‘significant’ chains within our proposed patent priority network. We suggest that the ‘critical’ and ‘significant’ chains that are created within the above network provide companies with important information which will ultimately provide them with valuable support for the subsequent decision of their patent portfolio strategies.     

Coalition Formation and Potential Games

In this paper we study the formation of coalition structures in situations described by a cooperative game. Players choose independently which coalition they want to join. The payoffs to the players are determined by an allocation rule on the underlying game and the coalition structure that results from the strategies of the players according to some formation rule. We study two well-known coalition structure formation rules and show that for both formation rules there exists a unique component-efficient allocation rule that results in a potential game. Journal of Economic Literature Classification Numbers: C71, C72.     

What to maximize if you must

The assumption that decision makers choose actions to maximize their preferences is a central tenet in economics, often justified formally or informally by appealing to evolutionary arguments. In contrast, we show that in almost every game and for almost every family of distortions of a player's actual payoffs, some degree of this distortion is beneficial to the player, and will not be driven out by any evolutionary process involving payoff-monotonic selection dynamics. Consequently, under any such selection dynamics the population will not converge to payoff-maximizing behavior. We also show that payoff-maximizing behavior need not prevail when preferences are imperfectly observed.     

Job contact networks

Many workers hear about or obtain their jobs through friends and relatives. The aim of this paper is twofold. First, we relate both individual and aggregate labor market outcomes to the network structure of personal contacts. Second, we study strategic network formation. To this purpose, we develop a model specifying at the individual level both the decision to form contacts with other agents, and the process by which information about jobs is obtained and transmitted. We show that equilibrium networks always exist and that only moderate levels of network asymmetry can be sustained at equilibrium. Also, we establish a general non-monotonicity result on information flow and unemployment with respect to network size in symmetric networks.     

Strategic positioning of global manufacturing virtual networks in the aeronautical industry

The evolution of organisations that work in multinational environments has considerably altered their production strategies. One of the consequences has been the appearance of global manufacturing virtual networks (GMVNs), which include all kinds of production centres. These networks establish a new type of vertical and horizontal collaboration between independent companies or even competitors who launch occasional collaborations on projects they could not take on individually. The purpose of this paper is to analyze the main reasons that determine the formation of GMVNs as well as the strategy of the companies involved in these organizations and how GMVN will evolve in the future. For that purpose, a conceptual framework is proposed based on four network features: strategy, structure, communication systems and culture. This work will delve into the strategy network feature by applying a strategic positioning model to a practical case in the aeronautical industry to gain a better understanding of how GMVNs work, its effectiveness by clarifying and putting these organisations in perspective and how they may evolve in the future.     

Radical changes in inter-organizational network structures: The longitudinal gap

The main goal of the research presented in this paper is to provide an overview of the available insights concerning radical changes in inter-organizational network structures. The following research question has been formulated: what is known about the way organizations in networks deal with, and are affected by, radical changes in inter-organizational network structures?In order to answer this question, a review of the most relevant literature dealing with changes in network structure over time is presented. The literature reviewed has been analyzed by comparing the role of change in the analysis (independent vs. dependent variable) as well as the manner in which change is conceptualized (incremental vs. radical change and dyadic vs. network change).It is found that studies that observe networks changing over time are scarce. Nevertheless, the available studies provide some interesting insights concerning the formation, evolution and termination of dyadic ties, network evolution, and the effects of (radical) changes in network structure. However, more research on several specific topics seems necessary. These topics are: the link between dyadic change and change at the network level, the evolution of network structures, the processes through which critical events lead to changes in network structures, and the effects of radical changes in network structures.     

Barriers to network-specific investment

We examine incentives for network-specific investment and consider the implications for network governance. We model a two-sided market in which participants making payments over a network platform can invest in a technology that reduces the marginal cost of using the platform. A network effect results in multiple equilibria—either all agents invest and use of the platform is high or no agents invest and use of the platform is low. The high-use equilibrium can be implemented if commitment is feasible. When the platform cannot commit to usage fees, investment in the platform-specific technology will be held up, thus implementing the low-investment equilibrium. As a result, governance structures necessary to achieve commitment will be preferred to those necessary merely to achieve coordination. For example, mutual ownership by users of a network platform may emerge where users face risk of ex post renegotiation. Such a governance structure will also be sufficient to avoid low investment attributable to the network effect.     

Unique stability in simple coalition formation games

We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterization of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterization using a graph representation, explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.