Abstract
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.
Highlights
Social networks play a vital role in the diffusion of information across society in setting as diverse as referral networks for jobs (Granovetter, 1974) and assessing quality of products ranging from cars to computers (Rogers an Kincaid, 1981)
We focus on the impact of the introduction of both decay and players heterogeneity on the architectures of networks that will be formed in equilibrium
In this payoff function we take into account the three following assumptions: (i) the value that player i obtains from player j does not depend on the group of j, (ii) the value that player i obtains from player j depends on the distance between i and j, and (iii) the cost that player i incurs for a link with player j depends on whether i and j belong to the same group or not
Summary
Social networks play a vital role in the diffusion of information across society in setting as diverse as referral networks for jobs (Granovetter, 1974) and assessing quality of products ranging from cars to computers (Rogers an Kincaid, 1981). Our paper deals with the two-way flow connections model introduced by Bala and Goyal (2000a) In this model a player i can access a player j directly by forming a costly link with j. The authors introduce heterogeneity of players in the two-way flow model of Bala and Goyal (2000a) They assume that players belong to different groups and costs of forming links within groups is lower than costs of forming inter-groups links. We show that in this situation the set of non-empty strict Nash networks is larger than in GGK (2006) It includes three other types of architectures in addition to interlinked periphery-sponsored stars networks. It is worth noting that decay is just one way of modelling deficiencies in information transmission Another way is to introduce imperfect reliability of links (see Bala and Goyal, 2000b, for a paper dealing with this).
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