A Nash bargaining model for simple exchange networks

Abstract

Starting from exogenously given negotiation networks, sociological exchange theories explain bilateral divisions of fixed surpluses (e.g., cake, dollar) as consequences of the partners' structural embeddedness. In accordance with the available experimental evidence, we focus on simple exchange networks and present a formal model for predicting profit splits from such structures. In contrast to other approaches, we combine the generalized Nash bargaining solution from game theory with the assumption that both relational features and network positions affect exchange outcomes

Sequential Power-Dependence Theory

“…What we borrow here is the idea that actors exchange according to an equal gain principle relative to some well-defined conflict points. This corresponds with the Nash solution (Nash 1953) in general bargaining theory (see also Braun and Gautschi 2006;Van Assen 2001: ch. 7 provides an extensive overview of the commonalities between network exchange theories and more general bargaining principles).…”

A behavioral study of bargaining in social networks

“…We were partly inspired by a long line of previous theoretical work which tried to relate wealth to network topology in bargaining settings [8,9,2,14,4,13,1,5]. A notable feature of these theories is the prediction that there may be significant local variation in splits purely as a result of the imposed deal limits and structural asymmetries in the network.…”

“…[4]), has been studied for decades. Several theoretical models have been designed to predict or propose how wealth should be divided [9,14,8,16], and human subject experiments have been conducted on a few small graphs (up to 6 nodes) [6,7,16], albeit with different interfaces and mechanisms than ours.…”

“…A few models are based strongly on notions of game-theoretic rationality and are natural extensions of standard economic literature to social networks. Two models that belong to this class were introduced by Cook and Yamagishi [8] and by Braun and Gautschi [4]. We shall mainly focus on these two models.…”

“…The model given by Braun and Gautschi [4] defines a "bargaining power function" on nodes that depends only on the degree of the node and degrees of its neighbors. This function increases with increase in degree of the node, and decreases with increase in degrees of its neighbors, and is independent of all other network aspects.…”