Christophe Bravard

NASH NETWORKS WITH IMPERFECT RELIABILITY AND HETEROGEOUS PLAYERS

This paper combines the imperfect reliability model of Bala and Goyal [2000b] with the heterogeneous player model of Galeottiet al.[2006]. We compare existence, characterization and efficiency results in the resulting framework with the results in other frameworks allowing for imperfect reliability or heterogeneity. Specifically, we compare our work with the framework of Haller and Sarangi [2005] which allows for heterogeneity in link reliability but assumes that players are homogeneous. We find, by contrast with their paper, that non existence of Nash networks is possible in our framework even if the population is very small. Moreover, although the incentives of players to maintain (or delete) links are different, in both frameworks there exist parameters such that every essential network is strict Nash and efficient. (This abstract was borrowed from another version of this item.)

A note on networks of collaboration in multi-market oligopolies

In this note, we extend the Goyal and Joshi’s model of collaboration networks in oligopoly to multi-market situations. We examine the incentive of firms to form links and the architectures of the resulting equilibrium networks in this setting. We then present some results on efficient networks.

The Insider-Outsider Model Reexamined

In this note we introduce different levels of decay in the Goyal, Galeotti and Kamphorst (GGK) insider-outsider model of network formation. First, we deal with situations where the amount of decay is sufficiently low to avoid superfluous connections in strict Nash networks and we examine the architectures of strict Nash networks. We show that centrality and small diameter are robust features of strict Nash networks. Then, we study the Nash and efficient networks when the decay vanishes.

Existence of Nash Networks and Partner Heterogeneity

In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by Bala and Goyal (2000a,b) in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the payoff function to find conditions under which Nash networks always exist. We provide two properties—increasing differences and convexity in the first argument of the payoff function that ensure the existence of Nash networks. Note that the commonly used linear payoff function satisfies these two properties.

Spying in Multi-Market Oligopolies

We consider a multimarket framework where a set of firms compete on two interrelated oligopolistic markets. Prior to competing in these markets, firms can spy on others in order to increase the quality of their product. We characterize the equilibrium espionage networks and networks that maximize social welfare under the most interesting scenario of diseconomies of scope. We find that in some situations firms may refrain from spying even if it is costless. Moreover, even though spying leads to increased product quality, there exist situations where it is detrimental to both consumer welfare and social welfare.

On the Interaction between Heterogeneity and Decay in Two-way Flow Models

In this paper we examine the role played by heterogeneity in the popular “connections model” of Jackson andWolinsky (1996). We prove that under heterogeneity in values or decay involving only two degrees of freedom, all networks can supported as Nash. Moreover, we show that Nash networks may not always exist. In the absence of decay, neither result can be found in a model with value heterogeneity. Finally, we show that on reducing heterogeneity, both the earlier “anything goes” result and the non-existence problem disappear.

A Note on Networks of Collaboration in Multi-market Oligopolies

In this note, we extend the Goyal and Joshi’s model of network of collaboration in oligopoly to multi-market situations. We examine the incentive of firms to form links and the architectures of the resulting equilibrium networks in this setting. We also present some results on efficient networks.

Local Spillovers, Convexity and the Strategic Substitutes Property in Networks

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.

Resources Flows Asymmetries in Strict Nash Networks with Partner Heterogeneity

This paper introduces a partner heterogeneity assumption in the one-way flow model of Bala and Goyal (2000, [1]). Our goal consists in the characterization of strict Nash networks with regard to the set of resources obtained by players. We use the notion of condensation network which allows us to divide the population in sets of players who obtain the same resources and we order these sets according to the resources obtained. Accordingly, we can examine the relationship between heterogeneity and asymmetries in networks. We establish that the nature of heterogeneity plays a crucial role on asymmetries observed in equilibrium networks.

Extending Networks of Collaboration to Multi-market Oligopolies

In this article, we extend the Goyal and Joshi’s model (2003) of network of collaboration in oligopoly to multi-market situations. We examine the incentive of firms to form links and the architectures of the resulting networks in this setting. We also present some results on efficient networks.