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The Insider-Outsider Model Reexamined

Pascal Billand, Christophe Bravard, Sudipta Sarangi

2010
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Games
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... von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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. 424 model without decay of GGK (2006). Second, we refine the result of GGK (2006) by assuming that the decay is sufficiently close to 1. More precisely, the class of interlinked periphery-sponsored stars networks, that the authors show as the unique non-empty strict Nash network contains two types of architectures. In the first one, the inter-groups link is sponsored by the center of a star, while in the second one this link is sponsored by a periphery player. We show that if the amount of decay is very low, then the second type of architecture cannot be strict Nash networks. So only the first type of architecture can be non-empty strict Nash networks. This result is important since it shows that strict Nash networks are also efficient networks when the amount of decay is low enough. 4 The rest of the paper is organized as follows. In Section 2, we present the framework of our model. Section 3 addresses the results that we obtain and Section 4 concludes. Model Setup We consider a society in which individuals are divided into pre-specified groups and costs of forming links within the groups are lower as compared to costs of forming inter-groups links. To simplify, we assume that there are only 2 groups. Let N t = {1 t , 2 t , . . . ,n t } be the set of players belonging to group t, t ∈ {0, 1}. The set of players is N = N 0 ∪ N 1 . As in GGK (2006) , we assume that |N 0 | = |N 1 | =n ≥ 4. 5 In the following we will assume that players who belong to the same group are similar and players who belong to different groups are different. In this paper the fact that two players are similar will allow them to have relationships which are less costly than the relationships between two players who are different. Indeed, if two players are similar they can communicate quickly (they speak the same language), while if two players are different (they speak different languages) the communication takes time and is most costly. Each player i ∈ N is assumed to possess some information of value to other players. She can augment her information by communicating with other people. This communication is made possible via pair-wise links. A strategy of player i t ∈ N t , t ∈ {0, 1}, is a vector g i t = (g i t ,1 t , . . . , g i t ,(i−1) t , g i t ,(i+1) t , . . . , g i t ,n t , g i t ,1 1−t , .

doi:10.3390/g1040422
fatcat:dlrrfpzjefdpbexvcbx2u6ybs4